Chapter 4.5, Problem 48PPS

To determine

To find: the addition area that will make dining room square and area of 250 square feet.

Answer to Problem 48PPS

About $\text{2}\text{.81}$ feet need to be added on each side.

Explanation of Solution

Given:

Dining room: $\text{13}\times \text{13}$ feet.

Customer like the Dining room area of $250$ square feet square shaped.

Concept used:

The square root property is one method that can be used to solve the quadratic equations, this method is generally used on equations that have form ${\text{ax}}^{\text{2}}\text{+bx+c}\text{or}{\left(\text{ax+b}\right)}^{\text{2}}\text{=c}$ ,or an equation that can be expressed in either or those forms.

All need to do is take a square root of both sides and solved for the variable.

Calculation:

Use the square root property in order to solve the equation:

  ${\left(\text{x+13}\right)}^{\text{2}}{\text{=5}}^{\text{2}}\text{×100}$ .

Using square root property:

  $\sqrt{{\left(\text{x+13}\right)}^{\text{2}}}\text{=±}\sqrt{{\text{5}}^{\text{2}}\text{×100}}$ .

  $\left(\text{x+13}\right)\text{=±5}\sqrt{\text{10}}$ .

Subtract $\text{13}$ from both side:

  $\text{x=5}\sqrt{\text{10}}-13$ and $\text{x=-5}\sqrt{\text{10}}-13$ .

  $\text{x=2}\text{.81}$ and $\text{x=-28}\text{.81}$

Hence, about $\text{2}\text{.81}$ feet need to be added on each side.