SOLUTION: The area of rectangle is thrice that of square Length of the rectangle is 40 cm & breath of the rectangle is 3/2 times that of the side of the square ? Find what is the side of

Algebra ->  Rectangles -> SOLUTION: The area of rectangle is thrice that of square Length of the rectangle is 40 cm & breath of the rectangle is 3/2 times that of the side of the square ? Find what is the side of       Log On


   

Question 895440: The area of rectangle is thrice that of square
Length of the rectangle is 40 cm & breath of the rectangle is 3/2 times that of the side of the square ?
Find what is the side of square in cm ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Square of side s, and rectangle of sides x and y.

s%5E2=3xy;
x=40, assigning x as length of the rectangle;
y=%283%2F2%29s.

Simplify using substitution for x=40.
s%5E2=3%2A40y and y=%283%2F2%29s.
s%5E2=120y
More than one set of steps, but solving for s in the linear equation seems like a good way.
s=%282%2F3%29y
And substitute into the s^2 equation:
%28%282%2F3%29y%29%5E2=120y
%284%2F9%29y%5E2=120y
y%5E2=%289%2F4%29120y
y%5E2=9%2A30y
y%5E2=270y
y%5E2-270y=0
y%28y-270%29=0
y%3C%3E0 so the solution for y is highlight%28y=270%29.

Going back a few steps, notice s=(2/3)y
s=%282%2F3%29270
highlight%28s=180%29------side length of the square.