# The areas of two similar triangles are 72 cm2 and 162 cm2. what is the ratio of the lengths of their corresponding sides? how do you find it

Let the smaller triangle, the one with `72 cm^2` area has sides a, b and c. Let the perependicular height to the vertice opposite to length b be h. Then the area of the traingle can be given as,

`A = 1/2xxbxxh`

Therefore,

`72 = 1/2bh`

`bh = 144`

If the two triangles are similar, their corrsponding dimensions have same ratio. If we assume that ratio is `x` , then the corresponding dimensions of the larger triangle is `xb` and `xh` .

Therefore its area is given by,

`162 = 1/2 (xb) xx (xh)`

`324 = x^2bh`

But we know `bh = 144`

Then,

`324 = x^2 xx 144`

`x^2 = 2.25 = 9/4`

`x^2 = 3^2/2^2`

`x = 3/2`

Therefore the ration of the lengths of their corresponding sides is 1.5