Question

If the area of a triangle is $150m^2$ and base: height is $3:4$, find its height:

• A. $25cm$
• B. $35m$
• C. $20m$
• D. $Noneofthese$

Answer 1

The correct option is C $20m$

let the base and height be $3x$ and $4x$ respectively

Area of triangle is $=\frac{1}{2}\times base\times height$

hence,

$\begin{array}{c}\Rightarrow \frac{1}{2}\times 3x\times 4x=150\\ \Rightarrow 4x^2=100\\ \Rightarrow x=\sqrt{25}\\ \Rightarrow \pm 5\end{array}$

on putting the value of $x=5m$

height$4\times 5$

hence, we get

height$=20m$