Question

The area of two similar triangles $\Delta ABC$ and $\Delta DEF$ are 144 $c{m}^2$ and 81 $c{m}^2$ respectively If the longest side of larger $\Delta ABC$ be 36 cm then the longest side of the smaller triangle $\Delta DEF$ is

• A. 20 cm
• B. 26 cm
• C. 27 cm
• D. 30 cm

Answer 1

The correct option is C 27 cm

In similar triangle ABC & DBF
$\frac{AB}{De}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{ratioofAreaoftriangleABC}{ratioofAreaoftriangleDEF}$
THEN $\frac{9}{12}=\frac{x}{36}$ (where x is longest side of the smaller triangle )
So x=27 cm