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The areas of two similar triangles are $12$ ${cm}^{2}$ and $48$ ${cm}^{2}$ . If the height of the smaller one is $2.1$ $cm$ , then the corresponding height of the bigger one is

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4.41

cm

8.4

cm

4.2

cm

0.525

cm

answer is C.

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Detailed Solution

Given that areas of two similar triangles are

{12 cm}^{2}

and

{48 cm}^{2} .

We know that for similar triangles the ratio of areas is equal to the ratio of squares of corresponding heights.
Hence,

\frac{A_{1}}{A_{2}} = \frac{(h_{1})^{2}}{(h_{2})^{2}}

\Rightarrow \frac{12}{48} = \frac{(2.1)^{2}}{(h_{2})^{2}}

\Rightarrow (h_{2})^{2} = 4 \times (2.1)^{2}

\Rightarrow h_{2} = 2 \times 2.1

{\Rightarrow h}_{2} = 4.2 cm

.
Therefore, the corresponding height of the bigger one is

4.2 cm

.
Hence option 3 is the answer.

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