Question

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

Answer 1

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

Answer 2

Answer: 8

Step-by-step 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:

$a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32$

Our equation:

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

The picture below visually explains the problem

Hope this helps!