Chapter 11, Problem 11PT

To determine

To find: The value of x.

Answer to Problem 11PT

X=4 units

Explanation of Solution

Given information: Given area of triangle is 16 square units. Base of triangle is x+4 and height is x.

Calculation:

Area of triangle =16

  $\begin{array}{l}=\frac{1}{2}\times \text{base×height=16}\\ =\frac{1}{2}(x+4)\times x=16\\ =x^2+4x=32\\ =x^2+4x-32=0\\ =x^2+8x-4x-32=0\\ =x(x+8)-4(x+8)=0\\ =(x=8)(x-4)=0\\ =x+8=0,x-4=0\\ x=-8,x=4\\ -8\text{is}\text{not}\text{possible}\\ \text{Therefore}\text{x=4}\end{array}$

  $\begin{array}{l}=\frac{1}{2}\times \text{base×height=16}\\ =\frac{1}{2}(x+4)\times x=16\\ =x^2+4x=32\\ =x^2+4x-32=0\\ =x^2+8x-4x-32=0\\ =x(x+8)-4(x+8)=0\\ =(x=8)(x-4)=0\\ =x+8=0,x-4=0\\ x=-8,x=4\\ -8\text{is}\text{not}\text{possible}\\ \text{Therefore}\text{x=4}\end{array}$