Question

A rectangular building has an area of 1,110 square meters and a perimeter of 134 meters. What are the dimensions of the building?

Answer 1

30 by 37 meters

Explanation:

Refer to the attached image to understand where the following formulas came from.

`\text{Area,} \ A=1110 \ m^2\\\\\text{Perimeter,} \ P=134 \ m`

We have a system of equations

`\Longrightarrow \left \{ {{xy=1110} \atop {2x+2y=134}} \right.\\\\\text{Taking equation 2} \rightarrow 2x+2y=134\\\\\Longrightarrow 2x=134-2y\\\\\Longrightarrow x=67-y \\\\\text{Now taking equation 1} \rightarrow xy=1110\\\\ \Longrightarrow (67-y)y=1110\\\\ \Longrightarrow 67y-y^2=1110\\\\ \Longrightarrow y^2-67y+1110=0\\\\\Longrightarrow (y-37)(x-30)=0\\\\\Longrightarrow \boxed{y=37 \ m \ or \ 30 \ m }`

When y=37:

`x(37)=1110\\\\\Longrightarrow \boxed{x=30}`

When y=30:

`x(30)=1110\\\\\Longrightarrow \boxed{x=37}`

So, the dimensions of the building are 30 by 37 meters.

Answer 2

The dimensions of the rectangular building are 30 meters by 37 meters.