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The width of a rectangle is 5 inches, and the diagonal length of the rectangle is 25 inches. Which measurement is closest to the length of this rectangle in inches?.

User Ben Toh
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1 Answer

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We can use the Pythagorean Theorem to find the length. Diagonals of a rectangle divide the rectangle into two or four triangles. With one diagonal, a rectangle is divided into two right triangles since rectangles contain 4 right angles. So, because we have a right triangle, we can apply the Pythagorean Theorem.

Formula:

a^2+b^2=c^2, where a=leg 1, b=leg2, and c=hypotenuse.

Input the lengths into the formula; we are given a leg length and the hypotenuse length:

(5)^2+b^2=25^2

We must solve for b, which will be the length of the triangle of leg 2.

Simplify;

25+b^2=625

Subtract 25 from both sides to isolate “b:”

b^2=600

Take the square root of both sides to cancel out the power of 2 on “b:”

√b^2=√600

b≈24.494

I’m assuming we should round to the nearest inch, which would be 24 inches

So, the answer is 24in. or ≈ 24.494in. depending on what the question wants.
User Tiago Veloso
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