Problems w/o Solution

Question

A square window is framed by two rectangular shutters. Each shutter is as long as one side of the window and the width of each shutter is 40 cm less than its length. I the are covered by one of the shutters is 4500cm2 less than the area of the window, find the dimensions of a shutter. 

Answer 1

Hi Lauren,

 

It helps to draw and label pictures first to see how everything fits together.

 

First;

Let x = the side of the window; so

x² is the area of the windows

 

Let x = two of the sides of the shutter and x- 40 = to the other two sides; so

x(x - 40) or x² - 40x is the area of the shutters

 

Set each of the areas equal to each other including the added area information

 

x² = x² - 40x + 4500; subtract x2 from both sides

0 = -40x + 4500; add 40x to both sides

40x = 4500; divide 40 to both sides

x = 112.5cm and x - 40 = 72.5cm

 

So the shutters dimensions are 112.5cm X 112.5cm - 40cm or 112.5cm X 72.5cm

 

Check

112.5² = 112.5² - 40(112.5) + 4500

12656.25 = 12656.25

 

I hope this was helpful.

 

Sincerely,

Patrick S.