SOLUTION: Three congruent rectangles are placed to form a larger rectangle with an area of 1350 sq cm. Find the area of a square that has the same perimeter as the larger rectangle. the pic

Click here to see ALL problems on Rectangles

Question 432737: Three congruent rectangles are placed to form a larger rectangle with an area of 1350 sq cm. Find the area of a square that has the same perimeter as the larger rectangle. the picture is set up like a rectangle on end next to 2 rectangles stacked on top of each other hamburger-like. here is the pic:
http://webpages.charter.net/beretsky/geo-01.JPG
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

In order for the three small rectangles to be congruent, the long side of each of the small rectangles must measure twice the short side. Let represent the measure of the short side, then the measure of the long side must be . Labling the sides leads us to the conclusion that the short side of the large rectangle is and the long side is .

The area of the larger rectangle is then times , or . But we know this to be equal to 1350 .

Solving for :

The perimeter of the large rectangle is:

But since we know that , the perimeter of the large rectangle must be 150 cm.

A square with an equal perimeter must have sides that measure 150 divided by 4 which is 37.5 cm.

The area of such a square is

Since your original measurement, namely the area of the large rectangle was given accurate to the nearest square centimeter, you must present your answer to the same precision.

John

My calculator said it, I believe it, that settles it