Question

The area of a square garden is 200 m2. How long is the diagonal?

20 m
10.2 m
200 m
100 m

Answer 1

First find the lenght of a side:

`a=√(200)\implies a\approx 14.14`

Then multiply the approximated side by
`√(2)` and obtain the lenght of diagonal:

`d\approx14.14√(2)=\boxed{20\mathrm{m}}`

Hope this helps.

Answer 2

20 m

Explanation:

First find the side length

A = s^2 for a square garden

200 = s^2

Take the square root of each side

sqrt(200) = sqrt(s^2)

sqrt(2) sqrt(100) = s

10 sqrt(2) = s

Now we can use the Pythagorean theorem to find the diagonal

a^2 + b^2 = c^2 where a and b are the side lengths a c is the hypotenuse

s^2 + s^2 = c^2

200 + 200 =c^2

400 = c^2

Take the square root of each side

sqrt(400) = sqrt(c^2)

20 = c