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10 votes
The length of a diagonal in a square is
32 inches. Find the perimeter of
the square.

1 Answer

9 votes
Drawing a diagonal line through a square or rectangle makes 2 right triangles. The line drawn will be the hypotenuse of the triangles, which is the longest side.

By using Pythagorean theorem we can solve for any of the side lengths of a triangle.

a will be the first side,
b will be the second side,
c will be the hypotenuse

And since the shape is a square, that means a and b will be the same length.

a^2 + b^2 = c^2

a^2 + b^2 = 1024

Since and b are the same, we can combine the left side of the equation to be 2a^2

2a^2 = 1024

Divide both sides by 2

a^2 = 512

Square root both sides

a = 22.6274

We have now solved for the length of one of the sides of the square. Since a square has 4 equal sides, we multiply this by 4 for our answer.


22.6274 x 4 = 90.5096 inches
User Sherrine
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