Question

The base and height of a triangle are in the ratio 4 : 5 and its area is 160 m². What is the height of the triangle?

• A. 15 m
• B. 10 m
• C. 20 m
• D. 25 m

Answer 1

The correct option is C 20 m

Let the base of the triangle be 4x and height be 5x.
Area of a triangle = $\frac{1}{2}$ x base x height
So, the area of the triangle = $\frac{1}{2}$ x 4x x 5x
This area is equal to the given area = 160 $m^2$
$\Rightarrow$160 = $\frac{1}{2}$ x 4x x 5x
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ 320 = 20 $x^2$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^2$ = 16
$\Rightarrow$ x = 4
So, the base = 4 x = 4 x 4 = 16 m
and height = 5 x = 5 x 4 = 20 m