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
BaLLatris [955]
2 years ago
12

Given square ABCD, with point P on side AB , point Q on side BC, point R on side CD, and point S on side DA as shown. Additional

ly, P is 2/3 of the way from A to B, Q is 2/3 of the way from B to C, R is 2/3 of the way from C to D, and S is 2/3 of the way from D to A. Compute the ratio of the area of square PQRS to the area of square ABCD. Write your answer as a fraction in lowest terms.
Mathematics
1 answer:
sveta [45]2 years ago
8 0

The ratio of the area of square PQRS to the area of square ABCD is 5/9

<h3>Area of square ABCD</h3>

Assume the measure of the side lengths of the square ABCD is 1, then the area of the square ABCD is:

A_1 = 1 \times 1

A_1 = 1

See attachment for the diagram that represents the relationship between both squares.

<h3 /><h3>Pythagoras theorem</h3>

The measure of length PQ is then calculated using the following Pythagoras theorem:

PQ^2 = (\frac 13)^2 + (\frac 23)^2

Evaluate the squares

PQ^2 =\frac 19 + \frac 49

Add the fractions

PQ^2 =\frac 59

<h3>Area of square PQRS</h3>

The above represents the area of the square PQRS.

i.e.

A_2 =\frac 59

So, the ratio of the area of PQRS to ABCD is:

Ratio = \frac{A_2}{A_1}

This gives

Ratio = \frac{5/9}{1}

Ratio = \frac{5}{9}

Hence, the ratio of the area of square PQRS to the area of square ABCD is 5/9

Read more about areas at:

brainly.com/question/813881

You might be interested in
Barry is trying to calculate the distance between point E(3, 1) and point F(4, 7). Which of the following expressions will he us
Masteriza [31]
Barry will use the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(4 - 3)² + (7 - 1)²]
d = 6.08 units
7 0
3 years ago
Read 2 more answers
Could someone show me how to start this function in excel.
Mrac [35]
Attached is a screenshot of spreadsheet used to do this problem.

You will see the excel functions used for each column. The average score is highlighted in blue.

6 0
3 years ago
Y = –3x 6 y = 9 what is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)
Romashka [77]

we have

<u>The system of equations</u>

y=-3x+6 -------> equation 1

y=9 -------> equation 2

Substitute equation 2 in equation 1

9=-3x+6

subtract 6 both sides

9-6=-3x+6-6

3=-3x

Divide by -3 both sides

x=-1

the solution is the point (-1,9)

therefore

the answer is

the solution to the system of equations is the point (-1,9)


4 0
3 years ago
Read 2 more answers
The drama club is having a car wash as a fundraiser. They wash x cars at $5 each
Galina-37 [17]

<u>Answer:</u>

x + y ≥ 26 + 15

5x + 8y ≥ 250 (see below)

Step-by-step explanation:

First, write an equation to represent the total cost to wash cars:

$5x = cost for cars

Then, write another for trucks:

$8y = cost for trucks

If the question is saying that they will wash at least 26 cars and 15 trucks, that means they could wash more. This means that we'll need an inequality:

This inequality represents that the total number of cars and trucks they wash will be at least—which means that it is equal to or greater than—than the amount given:

x + y ≥ 26 + 15

Any equation or inequality with two unknowns is not solvable, meaning we need a system of equations:

If they make at least $250, that means that we need to combine the costs of the cars and trucks to make an inequality:

5x + 8y ≥ 250

Now you have your system of equations:

x + y ≥ 26 + 15

5x + 8y ≥ 250

8 0
3 years ago
A movie theater seating is arranged with 15 seats in the front row, 14 seats in the middle row, and 26 seats in the back row. Th
Kryger [21]

Answer:

3/11

Step-by-step explanation:

i did this question it 3/11

6 0
3 years ago
Other questions:
  • Two angle measures in a triangle are 42° and 39°. What type of triangle is it?
    7·2 answers
  • (1)5x+11X<br><br>(2)-2(x-5)<br>using the distributive property
    7·1 answer
  • Describe the end behavior of the following function: f(x)=7x^2-3x^2-6
    12·1 answer
  • PLZ HELP I AM GONNA FAIL JUST EXPLAIN WHAT TO DO ​
    10·1 answer
  • The triangle shown below has an area of 20 units squared. Find the missing side if the height is 8
    10·2 answers
  • Dylan opens a credit card account with $550.00 of available credit .Now that he has made some purchases Dylan’s account only has
    14·1 answer
  • Kathy is buying 7 apples that cost $0.89 each, 2 oranges that are 1.12 each, and 1 pineapple that is $3.56. If she pays with a $
    8·1 answer
  • 5. Solve the equation 31.8 = 5W-6.7.​
    14·2 answers
  • A train travels 18 kilometers in 12 minutes. At this rate, how far does the train travel in 1 minute?
    10·1 answer
  • The base of a triangle is 13cm and its height is 5cm. what is the area of the triangle
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!