Chapter 11.1, Problem 27PPS

To determine

To Find: To find the base and height of the given triangle.

Answer to Problem 27PPS

The answer is 11m and 8m.

Explanation of Solution

Given information: Given area of triangle is 44square feet

Formula used: Area of triangle $=\frac{1}{2}\times \text{base}\times \text{height}$

Calculation:

Let the base of the triangle is x then, height is $(x-3)$

According to question.

  $\begin{array}{l}44=\frac{1}{2}\times x\times (x-3)\\ 88=x^2-3x\\ x^2-3x-88=0\\ x^2-11x+8x-88=0\\ x(x-11)+8(x-11)=0\\ (x-11)(x+8)=0\\ x=11\text{or}x=-8\\ \because \text{side}\text{cannot}\text{be}\text{negative}\\ \therefore x=11\end{array}$

Thus, the required base is 11meter.

And the height is $11-3=8$ meter

Hence, the required base and height of the triangle is 11meter and 8meter.