Chapter 10.3, Problem 36E

To determine

To solve the equation.

Answer to Problem 36E

  $x=8$

Explanation of Solution

Given information: $Area=\sqrt{5x-4}$ , $height=\sqrt{3x+12}$ and $base=2$

Formula Used: $Area=\frac{1}{2}\times base\times height$

Calculation:

  $Area=\sqrt{5x-4}$ , $height=\sqrt{3x+12}$ and $base=2$

  $Area=\frac{1}{2}\times base\times height$

  $\sqrt{5x-4}=\frac{1}{2}\times 2\times \sqrt{3x+12}$

Now, squaring both sides

  ${\left(\sqrt{5x-4}\right)}^2={\left(\sqrt{3x+12}\right)}^2$

So, simplify

  $5x-4=3x+12$

Now,

  $5x-3x=12+4$

So,

  $2x=16$

Hence,

  $x=8$