Dimensions of a rectangle....

Question

The perimeter of a rectangle is 3030, and its diagonal is √125. Find its dimensions and area, accurate to two decimal places.

Long side=

Short side=

Area=

Answer 1

I think that you meant that the perimeter is 30 and not 3,030.

 

If you call one side x and the other side y, then the perimeter is 2x+2y = 30 or(by dividing by 2) x+y=15,

 

This means that y = 15 - x.

 

So the length and widy can be represented by x and 15-x.

 

You can then use the Pythagorean Theorem to write

 

x² + (15-x)² = (√125) ²

x² + 225-30x+x²  = 125

2x² -30x +100 = 0

x² - 15x + 50 =0

(x-5)(x-10) =0

x=5 or x=10

 

So plugging these in gives you the same dimensions in this case....the length is 10 and the width is 5.

 

Hope this helped.