Chapter 4, Problem 56SGA

To determine

Find the dimensions of the window.

Answer to Problem 56SGA

  $21inches\times 15inches$ .

Explanation of Solution

Given information:

A special gloss paint covers the area of window to make it like glass. If the gloss covers area $315square$ inches and the window must be $6inchestaller$ than width.

Calculation:

Consider the given dimensions,

  $\begin{array}{l}Area=315squareinched\\ width=x\\ length=x+6\end{array}$

The formula of area for rectangular window is,

  $\begin{array}{l}A=length\times width\\ 315=\left(x+6\right)x\\ 315=x^2+6x\\ x^2+6x-315=0\\ x^2+21x-15x-315=0\left[factorizetheterm\right]\\ x\left(x+21\right)-15\left(x+21\right)=0\\ \left(x+21\right)\left(x-15\right)=0\\ x=-21,x=15\\ widthcannotbenegative\\ l=15+6=21inches\\ w=15inches\end{array}$

Hence, the dimensions are, $21inches\times 15inches$ .