Q36. - Geometry

Question

The base of a triangle is 1cm longer than its altitude. If the area of the triangle is$210c{m}^2$ , how long is the altitude ?

Step-by-Step Solution

Answer

The length of the altitude is20 cm.

Step 1. Analyze the given information.

The area of triangle $A=210c{m}^2$

Let the altitude bex .

According to the question,

The base of a triangle is1cm longer than its altitude, then the base of triangle will be $b=x+1$

Step 2. Concept Used.

Area of triangle can be found using the formula

$A=\frac{1}{2}bh$

Where, b= base and h= height of triangle.

Step 3. Use formula of the area of triangle.

$\begin{array}{l}A=\frac{1}{2}bh\\ A=\frac{1}{2}(x+1)\left(x\right)\\ 210=x^2+x\\ x^2+x-210=0\\ (x+21)(x-20)=0\\ x=-21,20\end{array}$

Since the length can not be negative,

Therefore, the length of the altitude is20cm .