1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
GenaCL600 [577]
3 years ago
10

A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congru

ent right triangles with areas of 44 in.²
Mathematics
1 answer:
kolezko [41]3 years ago
3 0

The length and width of the rectangle is 11 in and 8 in respectively.

Step-by-step explanation:

Given,

The width of a rectangle is 3 in less than the length.

The area of each congruent right angle triangle = 44 in²

To find the length and width of the rectangle.

Formula

The area of a triangle with b base and h as height = \frac{1}{2}bh

Now,

Let, the width = x and the length = x+3.

Here, for the triangle, width will be its base and length will be its height.

According to the problem,

\frac{1}{2}×(x+3)×x = 44

or, x^{2} +3x = 88

or,x^{2} +3x-88 = 0

or, x^{2}+(11-8)x-88 = 0

or, x^{2}+11x-8x-88 =0

or, x(x+11)-8(x+11) = 0

or, (x+11)(x-8) = 0

So, x = 8 ( x≠-11, the length or width could no be negative)

Hence,

Width = 8 in and length = 8+3 = 11 in

You might be interested in
Here james and stuff i need this
Wittaler [7]

Answer:

The Cost Price will be $19.99

Step-by-step explanation:

James

Sale Price = (100 - Discount Rate) x Cost Price

Let Y = Cost Price

By Putting the values in above equation:

$16.99 = (100 - 15) x Y

$16.99 = 0.85Y

Dividing the equation by 0.85, we get

Y = $16.99 / 0.85

Y = $19.99

4 0
3 years ago
State if the two triangles are congruent, if they are state how you know.
Mnenie [13.5K]

Answer:

I belive it would be HL because its defenitly not SSS

Step-by-step explanation:

HL Postulate is if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

4 0
3 years ago
You want to get a Dodgers shirt for Opening Day. The shirt you want is $36. Luckily, it is marked 25% off. You will have to pay
OlgaM077 [116]

Answer:

Part A

= $9

Part B

= $3.24

Part C

= $30.24

Step-by-step explanation:

Part A

= 36÷100x25

= $9

Part B

=36÷100x9

=$3.24

Part C

=36-9

=27

Then

=27+3.25

= $30.24

6 0
2 years ago
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an a
Scrat [10]

Answer:

The answer is (C) 8

Step-by-step explanation:

First, let's calculate the length of the side of the square.

A_{square}=a^2, where a is the length of the side. Now, let's try to build the square. First we need to find a point which distance from (0, 0) is 10. For this, we can use the distance formula in the plane:

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} which for x_1=0 and y_1 = 0 transforms as  d=\sqrt{(x_2)^2 + (y_2)^2}. The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, x_2, y_2 and 10 are a Pythagorean triple. From this, x_2= 6 or  x_2=8 while y_2= 6 or y_2=8. This leads us with the set of coordinates:

(\pm 6, \pm 8) and (\pm 8, \pm 6).  (A)

The next step is to find the coordinates of points that lie on lines which are perpendicular to the lines that joins the origin of the coordinate system with the set of points given in (A):

Let's do this for the point (6, 8).

The equation of the line that join the point (6, 8) with the origin (0, 0) has the equation y = mx +n, however, we only need to find its slope in order to find a perpendicular line to it. Thus,

m = \frac{y_2-y_1}{x_2-x_1} \\m =  \frac{8-0}{6-0} \\m = 8/6

Then, a perpendicular line has an slope m_{\bot} = -\frac{1}{m} = -\frac{6}{8} (perpendicularity condition of two lines). With the equation of the slope of the perpendicular line and the given point (6, 8), together with the equation of the distance we can form a system of equations to find the coordinates of two points that lie on this perpendicular line.

m_{\bot}=\frac{6}{8} = \frac{8-y}{6-x}\\ 6(6-x)+8(8-y)=0  (1)

d^2 = \sqrt{(y_o-y)^2+(x_o-x)^2} \\(10)^2=\sqrt{(8-y)^2+(6-x)^2}\\100 = \sqrt{(8-y)^2+(6-x)^2}   (2)

This system has solutions in the coordinates (-2, 14) and (14, 2). Until here, we have three vertices of the square. Let's now find the fourth one in the same way we found the third one using the point (14,2). A line perpendicular to the line that joins the point (6, 8) and (14, 2) has an slope m = 8/6 based on the perpendicularity condition. Thus, we can form the system:

\frac{8}{6} =\frac{2-y}{14-x} \\8(14-x) - 6(2-y) = 0  (1)

100 = \sqrt{(14-x)^2+(2-y)^2}  (2)

with solution the coordinates (8, -6) and (20, 10). If you draw a line joining the coordinates (0, 0), (6, 8), (14, 2) and (8, -6) you will get one of the squares that fulfill the conditions of the problem. By repeating this process with the coordinates in (A), the following squares are found:

  • (0, 0), (6, 8), (14, 2), (8, -6)
  • (0, 0), (8, 6), (14, -2), (6, -8)
  • (0, 0), (-6, 8), (-14, 2), (-8, -6)
  • (0, 0), (-8, 6), (-14, -2), (-6, -8)

Now, notice that the equation of distance between the two points separated a distance of 10 has the trivial solution (\pm10, 0) and  (0, \pm10). By combining this points we get the following squares:

  • (0, 0), (10, 0), (10, 10), (0, 10)
  • (0, 0), (0, 10), (-10, 10), (-10, 0)
  • (0, 0), (-10, 0), (-10, -10), (0, -10)
  • (0, 0), (0, -10), (-10, -10), (10, 0)

See the attached second attached figure. Therefore, 8 squares can be drawn  

8 0
3 years ago
Find the interest of a $2,500 loan, with an interest rate of 7% compounded annually over
Ksenya-84 [330]
Interest = Principle(Rate)(Time)
2500(.07)(6) = 1050


The interest will be $1,050
3 0
3 years ago
Other questions:
  • Jayden makes a 5-sided spinner, numbered from 1 to 5. He records the number of times he scores a 3 from different numbers of spi
    14·1 answer
  • Tracy can wallpaper 7 rooms in a new house in 21 hours. together with her trainee they can wallpaper the 7 rooms in 12 hours. ho
    12·1 answer
  • Solve x2 − 8x + 15 < 0.
    13·1 answer
  • At Snack Shack, drinks cost $1.50. Write an expression that could be used to find the total cost in dollars of d drinks.
    7·1 answer
  • a survey was taken of children between the ages 7 and 12. let A be the event that the person rides the bus to school, and let B
    8·1 answer
  • For what value of x is the figure a rectangle?
    13·1 answer
  • How many times does the 8 fit into the 83
    9·2 answers
  • In the triangle XYZ, the measure of angle X is 68 , XY= 2.5
    8·1 answer
  • QUESTION 1 [21] 1.1 Danny and Refilwe are amateur photographers who attended the 2021 CAF Championship in Cameroon. The small bu
    15·1 answer
  • 5x + 3y = 26<br> 6x+ 7y=21
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!