SOLUTION: The perimeter of a square is 20 centimeters. Find the length of a diagonal.

Question 115244: The perimeter of a square is 20 centimeters. Find the length of a diagonal.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Sketch a square. Label each of its sides with 20. Then sketch in a diagonal. You will see
that the diagonal divides the square into two right triangles. Each of these triangles
has legs that are both 20 units long and the diagonal of the square is the hypotenuse
of the triangles.
.
This problem can be solved by using the Pythagorean theorem. (The Pythagorean theorem
applies only to right triangles.) The Pythagorean theorem says that the sum of the squares
of the two legs of a right triangle equals the square of the hypotenuse. In equation
form this is:
.
A^2 + B^2 = H^2
.
where A and B are the legs of the triangle. In this problem both A and B are 20. So
replace them with 20 and you get:
.
20^2 + 20^2 = H^2
.
But 20^2 is 400. Substitute that into the equation and you get:
.
400 + 400 = H^2
.
Do the addition on the left side and the equation becomes:
.
800 = H^2
.
Transpose this equation (switch sides):
.
H^2 = 800
.
Solve for H by taking the square root of both sides:
.

.
Then apply some rules of square roots to simplify the answer. The square root of a number
equals the square root of the product of its factors. So we can write:
.

.
Then the square root of a product of terms is equal to the product of the square roots of
each of the terms. So, we can further say:
.

.
But the square root of 400 is 20. So this further simplifies to:
.

.
So the answer to this problem is that the diagonal H of the square is:
.
centimeters
.
Hope this helps you to understand the problem.
.
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