Chapter SH, Problem 9.22EP

To determine

To solve equation by completing the square.

Answer to Problem 9.22EP

  $x=4.$

Explanation of Solution

Given information :

Height of triangle $(x+2)$ in.

Base of triangle $(x+8)$ in.

Area of triangle sq. inches

Formula used :

The area of a triangle is given by :-

  $(0.5)\times$ Base $\times$ Height $=$ Area.

To solve the equation by completing the square the $x^2$ and $x$ terms need to be isolated then the square is completed by adding the required constant to both sides of the equation.

Calculation :

  $\frac{1}{2}(x+2)(x+8)=36$

Simplifying.

  $x^2+10x+16=72$

The above expression can also be written as.

  $x^2+10x+25=72-16+25$

Completing the sqaure.

  ${(x+5)}^2=81$

Taking square root of both sides

  $x+5=\sqrt{81}$

Simplifying.

  $x=\pm 9-5$

Therefore, $x=4,-13$ .

Here, -13 is not considered as length cannot be negative.