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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

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