Chapter 5.3, Problem 69PPS

To determine

To calculate: The length of the base.

  

Answer to Problem 69PPS

The length of the baseis $13\text{ cm}$ .

Explanation of Solution

Given information:

The area of the triangle is $26$ square centimeters and figure,

  

Formula used:

Area of a triangle with base b and height h is half into the product of base and height which is mathematically expressed as,

  $\text{A}=\frac{1}{2}\times b\times h$

Calculation:

Consider the given information that area of the triangle is $26$ square centimeters and figure,

  

In the above figure, $h=x-2\text{ cm}$ , $b=x+7\text{ cm}$ and area is $26{\text{ cm}}^2$ .

Recall that area of a triangle with base b and height h is half into the product of base and height which is mathematically expressed as,

  $\text{A}=\frac{1}{2}\times b\times h$

Apply it,

  $\begin{array}{c}\text{A}=\frac{1}{2}\times b\times h\\ 26=\frac{1}{2}\times \left(x+7\right)\times \left(x-2\right)\\ x^2+7x-2x-14=26\times 2\\ x^2+5x-66=0\end{array}$ .

Factorize it further as,

  $\begin{array}{c}{x}^2+5x-66=0\\ x^2+11x-6x-66=0\\ x\left(x+11\right)-6\left(x+11\right)=0\\ \left(x-6\right)\left(x+11\right)=0\end{array}$

Since, value of base cannot be negative; value of $x=6$ .

So, the value of base is calculated as,

  $\begin{array}{c}b=x+7\\ =6+7\\ =13\text{ cm}\end{array}$

Thus, the length of the baseis $13\text{ cm}$ .