Question

The area of a square is 81square centimeters. First, find the length of a side. Then, find the length of the diagonal?

Answer 1

Part 1:

The length of a side is 9 cm.

The square root of 81 is 9. We have to find the square root bc we know it is a square.

Part 2:

The hypotenuse (or diagonal) is c.

Using the Pythagorean Theorem

`a^(2) + {b}^(2) = {c}^(2)`
you would know that 9 is a and b.


`{9}^(2) + {9}^(2) = {c}^(2)`
We know that

`{9}^(2) = 81`
so you add 81 to 81.


`81 + 81 = 162`
81 and 81 make 162.

So you know ...


`{c}^(2) = 162`
You take the square root of 162.


`√(162) = 12.73`
well almost.

You can write your answer as


`about \: 12.73 cm`
or

`√(162) cm`

Hope I helped!