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**

**Further Reading**