Question : Two triangles MNO and XYZ are given similar with the ratio of their side as 9 : 4. If the area of the larger triangle is 243 sq. cm, then the area of the smaller triangle will be:
Option 1: 162 sq. cm
Option 2: 28 sq. cm
Option 3: 48 sq. cm
Option 4: 16 sq. cm
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Correct Answer: 48 sq. cm
Solution :
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
Given that the ratio of the sides of triangles MNO and XYZ is 9 : 4.
$ \frac{\text{Area of $\triangle$XYZ}}{\text{Area of $ \triangle $MNO}}=(\frac{9}{4})^2 = \frac{81}{16}$
The area of triangle MNO (the larger triangle) is 243 sq. cm.
$\therefore\text{Area of $ \triangle $XYZ} = \frac{\text{Area of $ \triangle $MNO}}{\text{Area ratio}} = \frac{243 \times 16}{81} = 48 \text{ sq. cm}$
Hence, the correct answer is 48 sq. cm.
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