Question

A city counsel has a square lot to place a playground. They plan to place a diagonal of treesto create two distinct play areas. To determine if there is enough money in the budget, theyneeds to know the distance. If the length of each side of the lot is 32√7 m, how long is thediagonal?

Answer 1

Answer: 13.01m

Step-by-step explanation

A right triangle is a triangle with a 90º angle. If the square lot is divided by a diagonal, then two right triangles are formed:

The right triangle satisfies the Pythagorean Theorem:

`c^2=a^2+b^2`

where c is the diagonal (hypotenuse), and a and b are the sides. In our case, as it is a square, a = b, meaning:

`c^2=32√(7)+32√(7)`

Thus, simplifying and solving for c we can find the diagonal:

`c^2=2(32√(7))`
`√(c^2)=\sqrt{64√(7)}`
`c\approx13.01m`