Question

In the following exercises, solve the problem using a system of equations .

The perimeter of a rectangle is 58 meters and its area is 210 square meters. Find the length and width of the rectangle.

Short answer

Dimensions of rectangle

Length =15, width =14

or

Length =14, width =15

Step-by-step solution

Given information 

The perimeter of a rectangle is 58 meters and its area is 210 square meters. Find the length and width of the rectangle.

frame equations

Let x be the length of the rectangle

y be the width of the rectangle

The perimeter of a rectangle is 58 meters

$2x+2y=58$

Area of the rectangle is 210 square meters

$xy=210$

solve the equation for x

solve the first equation for y

$$\begin{gathered} 2x+2y=58 \\ Divideby2 \\ x+y=29 \\ y=29-x \\ Substituteitinsecondequation \\ xy=210 \\ x(29-x)=210 \\ 29x-x^2=210 \\ 29x=210+x^2 \\ 0=x^2-29x+210 \\ {x}^2-29x+210=0 \\ (x-14)(x-15)=0 \\ x-14=0 \\ x=14 \\ x-15=0 \\ x=15 \end{gathered}$$

substitute x values and find out y

$$\begin{gathered} y=29-x \\ x=14 \\ y=29-14 \\ y=15 \\ x=15 \\ y=29-15 \\ y=15 \end{gathered}$$

length and width 

Dimensions of rectangle

Length =15, width =14

or

Length =14, width =15