Question

Find the ratio of the area of two triangles on the same base if the ratio of their heights is $7$ is to $5$

• A. $\frac{7}{5}$
• B. $\frac{5}{7}$
• C. $\frac{12}{5}$
• D. $1$

Answer 1

Answer: (A)

$\frac{7}{5}$

Since, we know Area of a triangle$=\frac{1}{2}\times base\times height$

Let base of both triangles is $b$ and height of first triangle is $h1$, height of second triangle $h2$.

$\frac{\text{Area of 1st triangle}}{\text{Area of 2nd triangle}}=\frac{\frac{1}{2}\times b\times h1}{\frac{1}{2}\times b\times h2}=\frac{h1}{h2}$

Hence proved that the ratio of the area of two triangles with same base is equal to the ratio of their heights.

Hence answer is $\frac{7}{5}$