Question

If the measures of sides BC and AD are 6 cm and 12 cm respectively, then ratio of areas of ABOC and ADOA is: (a) 1:2 (b) 1:4 (c) 4:1 (d) 2:1​

Answer 1

Given:

If the measures of sides BC and AD are 6 cm and 12 cm respectively, then the ratio of areas of ABOC and ADOA is: (a) 1:2 (b) 1:4 (c) 4:1 (d) 2:1​

To find:

The ratio of areas of ABOC and ADOA is?

Solution:

We know,

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

i.e., $\boxed{\bold{\frac{Area \:of \triangle _1}{Area \:of \triangle _2} = \bigg(\frac{Side_1}{Side_2}\bigg)^2}}$

Considering Δ BOC ~ Δ DOA, we get

$\frac{Area \:of\: \triangle \:BOC}{Area \:of \:\triangle \:DOA} = \bigg(\frac{BC}{AD}\bigg)^2}}$

on substituting the value of BC = 6 cm and AD = 12 cm

$\implies \frac{Area \:of\: \triangle \:BOC}{Area \:of \:\triangle \:DOA} = \bigg(\frac{6}{12}\bigg)^2}}$

$\implies \frac{Area \:of\: \triangle \:BOC}{Area \:of \:\triangle \:DOA} = \frac{36}{144}}$

$\implies \bold{\frac{Area \:of\: \triangle \:BOC}{Area \:of \:\triangle \:DOA} = \frac{1}{4}}}$ ← option (b)

Thus, the ratio of areas of Δ BOC and Δ DOA is → 1 : 4.

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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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