Question

Areas of two similar triangles are 100 cm² and 64 cm². If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle​

Answer 1

Given:

Areas of two similar triangles are 100 cm² and 64 cm². If a side of the smaller triangle is 12 cm, then find the corresponding side of the bigger triangle

To find:

The corresponding side of the bigger triangle

Solution:

Let's say,

Δ ABC → bigger triangle → Area = 100 cm²

Δ PQR → smaller triangle → Area = 64 cm²

Side PQ = 12 cm

Here we have to find the length of AB

We know,

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Based on the above theorem, we get

$\frac{Area\: (\triangle ABC)}{Area \:(\triangle PQR)} = \bigg(\frac{AB}{PQ} \bigg)^2$

$\implies \frac{100\:cm^2}{64 \:cm^2} = \bigg(\frac{AB}{12} \bigg)^2$

$\implies \frac{25}{16} = \bigg(\frac{AB}{12} \bigg)^2$

$\implies \frac{25}{16} = \frac{AB^2}{144}$

$\implies AB^2 = 25 \times 9$

$\implies AB = \sqrt{5\times 5 \times 3\times 3}$

$\implies AB = 5 \times 3$

$\implies \bold{AB = 15 \:cm}$ ← length of the side of bigger Δ ABC

Thus, the corresponding side of the bigger triangle​ is → 15 cm.

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Also View:

Find the ratio of the areas of two similar triangles if two of their corresponding sides are of length 3 cm and 5 cm.

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the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

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