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  • Areas of two similar triangles are 36 cm 2 and 100 cm 2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle.

Areas of two similar triangles are 36 cm2 and 100 cm2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle.

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Answer : [12 cm ]

Given:- area of smaller triangle = 36 cm2

area of larger triangle = 100 cm2

length of the side of larger triangle = 20 cm

let the length of the corresponding side of the smaller triangle = x cm

According to the property of area of similar triangles,

\frac{ar\left ( \text {larger triangle} \right )}{ar\left ( \text {smaller triangle} \right )}=\frac{\left ( \text {side of larger triangle} \right )^{2}}{\left ( \text {Side of smaller triangle} \right )^{2}}

\frac{100}{36}=\frac{\left ( 20 \right )^{2}}{x^{2}}

x^{2}=\frac{20 \times 20 \times 36}{100}

x=\sqrt{144}

x=12\; cm

Posted by

infoexpert23

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