Question

If the area of a square is 32ft how long is the diagonal?

Answer 1

Answer: 8

Explanation:

To find the diagonal, we need to use two formulas:

Area of a square:
`A = s^(2)` (Area = side * side)

Pythagorean Theorem:
`a^(2) +b^(2) =c^(2)`

Since every side of a square is the same:

`a^2 = b^2\\a = b = √(32) \\a^(2) = 32\\b^2 = 32`

Our equation:

`32 + 32 = c^2\\64 = c^2\\8 = c`

The picture below visually explains the problem

Hope this helps!

Answer 2

8 FEET LONG

A square has the same length all 4 sides, therefore in order to find the length of the sides, you would need to find the square root of 32, which would be 5.66 or 4 radical 2. Then to find the diagonal length you would need to split the square diagonally resulting in 2 triangles. We know the side lengths of the triangles but not the hypotenuse( longest side of triangle), which is the diagonal length. To figure this out we would use the Pythagorean theorem a^2 + b^2 = c^2. We know what a and b are so we substitute, do basic algebra, and find that c is equal to 8