Question

The ratio of the two areas of two triangles with the common base is $6:5$. Height of the larger triangle is $9cm$. Then find the corresponding height of the smaller triangle.

• A. Height of the smaller triangle is $7.5cm$.
• B. Height of the smaller triangle is $6.5cm$.
• C. Height of the smaller triangle is $5.5cm$.
• D. Height of the smaller triangle is $4.5cm$.

Answer 1

The correct option is A Height of the smaller triangle is $7.5cm$.

Base of two triangles is the same. Height of first triangle is 9 cm.
$\frac{Area{△}_1}{Area{△}_2}=\frac{\frac{1}{2}b\times h_1}{\frac{1}{2}b\times h_1}$
$\frac{Area{△}_1}{Area{△}_2}=\frac{h_1}{h_2}$
$\frac{6}{5}=\frac{9}{h_2}$
$h_2=\frac{9\times 5}{6}$
$h_2=7.5$ cm