Question

If the area of a square is `225` `cm^2`, what is the length of the diagonal?

Answer 1

`slope=15sqrt(2)" "` as an exact value

`slope ~~21.213" "` to 3 decimal places`larr` approximate value

Explanation:

By Pythagoras`" " a^2+b^2=c^2`

Known that area is `axxb`

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`color(blue)("Determine the length of the sides")`

As this is a square the length of all the sides are the same.

Let the length of the sides be `x`

Given that the area is `225 cm^2` we have

`axxb->x xx x ->x^2 =225`

Square root both sides

`sqrt(x^2)=sqrt(225)`

`color(blue)(x=15)`
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Using Pythagoras

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

`=>x^2+x^2=c^2`

But `x^2+x^2 =2x^2`

`=>c^2=2x^2`

Square root both sides

`=>c=sqrt(2x^2)`

`=>c=xsqrt(2)`

But `x=15`

`=>c=15sqrt(2)" "` as an exact value

`=>c~~21.213" "` to 3 decimal places