Question

If the perimeter of a square is 24, find the length of a diagonal.

Answer 1

-- All 4 sides of a square have equal length.

-- If the perimeter of a square is 24, then each side is (24/4) = 6 long.

-- When you cut the square along the diagonal, you have

a right triangle, with both legs 6 long.

The diagonal of the square is the hypotenuse of the triangle.

-- The length of the hypotenuse is the square root of

(one leg squared) plus (the other leg squared).

In this triangle, that's (6² + 6²) = (36 + 36) = 72 .

So the length of the hypotenuse is √72 .

Let's simplify that:

√72

= √(36 · 2)

= √36 · √2

= 6 · √2

There you have it . . . something worth remembering:

The length of the diagonal of a square is always

the length of one side, multiplied by √2 .

Answer 2

Since all the sides are all the same length we have 24/4 = 6 as the length of each side.

A diagonal of a square is (length of one side of the square)(sqrt(2)

So we have 6sqrt(2) as the length of the diagonal