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

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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`


`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`


`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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