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
rodikova [14]
3 years ago
8

The perimeter of a rectangle is 84 feet. the length is two feet greater than 3 times the width. Find the length and width. Draw

and label a diagram.
Mathematics
1 answer:
Kipish [7]3 years ago
4 0
The formula for a rectangle's perimeter is

P = 2l + 2w

We know the length is 2 ft greater than thrice the width, so 2l becomes:

3w + 2ft + 3w + 2ft

Substitute.

P = 3w + 2ft + 3w + 2ft + 2w

Add like terms.

P = 8w + 4ft

Substitute P.

84 ft = 8w + 4ft

Subtract 4 ft from both sides to eliminate. (Property of equality)

84 ft - 4ft = 8w + 4ft - 4ft
80 ft = 8w

Divide 8 on both sides to isolate w.

80 ft / 8 = 8w / 8

10 ft = w

We have the value of w, now look for the l which we know is 2 feet more than thrice the value of w.

l = 10 ft × 3 + 2 ft
l = 30 ft + 2 ft
l = 32 ft

Therefore, the length and the width of the rectangle is 10 ft (w) and 32 ft (l).

Check:
84 ft = (2) (10 ft) + (2) (32 ft)
84 ft = 20 ft + 64 ft
84 ft = 84 ft ✔

♧
You might be interested in
Henrique drew and labeled the net shown. He also labeled the areas of the left and right triangular sides.
Oksana_A [137]

Answer: SA=117.2\ in^2

Step-by-step explanation:

You need to remember the following:

1. The area of a rectangle can be calculated with the following formula:

A_r=lw

Where "l" is the length and "w" is the width.

2. The area of a triangle can be calculated with the following formula:

A_t=\frac{bh}{2}

Where "b" is the base and "h" is the height.

Use those formulas to find the area of each face.

<u> Area of the rectangle</u>

A_r=(10\ in)(4\ in)=40\ in^2

<u>Area of two triangles</u>

There are two equal triangles. Each one has a base  of 10 inches and a height of 5 inches. Then, their areas are equal:

A_{t1}=A_{t2}=\frac{(10\ in)(5\ in)}{2}=25\ in^2

The areas of the other two triangles (which are equal) are:

A_{t3}=A_{t4}=13.6\ in^2

Adding the areas of the faces, you get that the surface area of the rectangular pyramid is:

SA=40\ in^2+25\ in^2+25\ in^2+13.6\ in^2+13.6\ in^2\\\\SA=117.2\ in^2

3 0
3 years ago
Read 2 more answers
What does 45 - 4x equal
xxTIMURxx [149]
Let y = 0 to find the x-intercept(s).

0 = 45 − 4x

*Then subtract 45 from both sides*
-45 = -4x

*Next, DIVIDE both sides by -4*

-45
—— = x
-4

*NEXT, realize that TWO NEGATIVES MAKE A POSITIVE *

45. 4
——— = x {FLIP} x=——-
4. 45.


y-Intercept

Let x = 0 to find the y-intercept(s).


y = 45 −4(0)

NEXT, SIMPLIFY:

y=45
7 0
3 years ago
Graph the line that passes through the points (4,-6) and (-4,-8) and determine the equation of the line.
allochka39001 [22]

Answer:

y=1/4x-7; can't put graph on here

Step-by-step explanation:

m=y2-y1/x2-x1

m=-8+6/-4-4=-2/-8=1/4

put it in point-slope form with (4,-6) as the base

y-y1=m(x-x1)

y+6=1/4(x-4)

y+6=1/4x-1

y=1/4x-7

7 0
2 years ago
Mark cycles from home to school at a speed of 16 kilometers per hour. He cycles back on the
katrin [286]

Answer:

Write a time equation, time = dist/speed

:

go time + return time = total time

d%2F16 + d%2F15 = 7.75 hrs

multiply equation by the least common multiple 240, cncel the denominators:

 

15d + 16d = 240(7.75)

31d = 1860

d = 1860/31

d = 60 km one way

total dist = 120 km

:

Check this, find the actual time each way

60/16 = 3.75 hrs

60/15 = 4 hrs

-----------------

total time 7.75 hrs

Step-by-step explanation:

7 0
2 years ago
What is the point called where 2 lines intersect or cross? It is the ___________ to the system of equations
Oxana [17]

Answer:

Step-by-step explanation:

The point where the lines intersect is called the point of intersection.These form opposite angles.

7 0
2 years ago
Read 2 more answers
Other questions:
  • What is 110 raised to the 76th power.
    9·1 answer
  • What is the graph of 3x + 5y = –15?
    7·2 answers
  • At Pizza hut, 9% of the pizzas made last week had extra cheese. if 27 pizzas had extra cheese, how many pizzas in all were made
    8·1 answer
  • A symmetric data distribution is shown. Which addition of data will have the greatest effect on the mean?
    5·1 answer
  • 3.47472 rounded to the nearest 10th
    11·2 answers
  • What is F(x)=-12/25(x-25)^2+32 in standard form?
    6·1 answer
  • Write 99 as a product of primes.<br> Use index notation when giving your answer.<br> Do
    14·1 answer
  • 50 POINTS !!<br><br><br> PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
    14·1 answer
  • A number less than 9 is more than -16
    10·2 answers
  • What is meaning of trigonometry ​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!