Question

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:

• A. $4.41$ $cm$
• B. $8.4$ $cm$
• C. $4.2$ $cm$
• D. $0.525$ $cm$

Answer 1

Answer: (C)

$4.2$ $cm$

Areas of two similar triangles are $12c{m}^2$ and $48c{m}^2$
For similar triangles the ratio of areas is equal to the ratio of square of corresponding heights
Hence, $\frac{A_1}{A_2}=\frac{(h_1{)}^2}{(h_2{)}^2}$

$\frac{12}{48}=\frac{(2.1{)}^2}{(h_2{)}^2}$

$(h_2{)}^2=4\times (2.1{)}^2$

$h_2=2\times 2.1$

$h_2=4.2cm$