Question

If the area of a triangle is $1176{cm}^2$ and base: corresponding altitude is $3:4$, then the altitude of the triangle is:

• A. $42cm$
• B. $52cm$
• C. $54cm$
• D. $56cm$

Answer 1

The correct option is B $52cm$

Ratio of base to altitude $3:4$

Area of triangle $=1176c{m}^2$

Let

Base $=3x$ and Altitude $=4x$

Area of triangle $=\frac{1}{2}\times$ Base $\times$ Altitude

$1176=\frac{1}{2}\times 3x\times 4x$

$12x^2=1176\times 2$

$12x^2=2352$

$x^2=\frac{2352}{12}$

$x^2=196$

$x=13$

So,

Base $=3\times 13=39cm$

Altitude $=4\times 13=52cm$