Question

The area of a square garden is 128 m2 how long is the diagonal?

Answer 1

If we know the area, we can first find the side length of this garden. The area of a square is the side length squared. So, we can write:

x^2 = 128

Square root both sides, and you get

x = sqrt (128)

The diagonal of the square is the side length times sqrt (2) because the diagonal plus two side lengths make a 45-45-90 triangle. So:

sqrt (128) * sqrt (2) = sqrt (256) = 16.

The length of the diagonal is 16 meters.

Answer 2

Answer with Step-by-step explanation:

Let s be the length of the side of the square garden

Then, Area=s²

The area of a square garden is 128 m²

i.e. s²=128 m²

s²=
`(2^3)^2* 2` m²

i.e. s=
`2^3√(2)\ m`

Also, the length of diagonal of a square is given by:

d=
`√(2)s`

=
`√(2)* 2^3* √(2)\ m`

=
`2^4\ m`

= 16 m

Hence, The length of diagonal of square garden is:

16 m