Question : The areas of two similar triangles ABC and PQR are 64 cm2 and 144 cm2, respectively. If the greatest side of the smaller ΔABC is 24 cm, then what is the greatest side of the bigger ΔPQR?
Option 1: 32 cm
Option 2: 24 cm
Option 3: 42 cm
Option 4: 36 cm
Correct Answer: 36 cm
Solution :
Given: The areas of two similar triangles ABC and PQR are 64 cm
2
and 144 cm
2
, respectively. The greatest side of the smaller ΔABC is 24 cm.
Let the greatest side of the bigger ΔPQR be $x$.
We know that, The ratio of the area of similar triangles = (The ratio of corresponding sides)
2
According to the question,
⇒ $\frac{64}{144}=(\frac{24}{x})^2$
⇒ $x^2=\frac{144×24×24}{64}$
$\therefore x=36$ cm
Hence, the correct answer is 36 cm.
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