Question

you are designing a patio for your backyard. you decide to mark it off using your tape measure. two sides are 21 feet long and two sides are 28 feet long. how can you ensure that the patio is a rectangle?

to ensure that the patio is a rectangle without measuring the angles, measure the diagonals. the diagonals of a rectangle must be congruent. you can find the length of the diagonals by using the pythagorean theorem.

(d^2 = 21^2 + 28^2)

if both diagonals are ft, you know the patio is a rectangle.

Explanation:

Set up the Pythagorean equation for the diagonal

$$ d^2 = 21^2 + 28^2 $$

Calculate the squares and sum

$$
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$$

Solve for the diagonal length

$$ d = \sqrt{1225} = 35 $$

Answer:

If both diagonals are <blank>35</blank> ft, you know the patio is a rectangle.