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
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