SOLUTION: Two rectangles are similar. The smaller has a length of 8cm and an area of 40cm^2. If the width of the larger rectangle is 10cm, find its area.

Algebra ->  Rectangles -> SOLUTION: Two rectangles are similar. The smaller has a length of 8cm and an area of 40cm^2. If the width of the larger rectangle is 10cm, find its area.      Log On


   

Question 893712: Two rectangles are similar. The smaller has a length of 8cm and an area of 40cm^2. If the width of the larger rectangle is 10cm, find its area.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The larger similar rectangle has linear dimensions k times the smaller rectangle.


Small rectangle, 8 cm by w cm.
Area, 8w=40


Larger rectangle, 8k cm by kw cm.
Area, 8k%2Akw;
but also is given that kw=10.


Find two equations with two unknowns!
8w=40 and kw=10.
First one gives w=40%2F8=5.
Using this in the second equation gives k%2A5=10 and therefore k=2.


Find the requested area for the larger rectangle.
8k%2A10
8%2A2%2A10
highlight%28160%2Acm%5E2%29