Question

The length of a rectangle is the square root of 100 times an unknown number, x. The width is one-half an unknown number, y, less three-halves x. If the area of the rectangle is 125 cm2, find an equation that would give the width of the rectangle given the length.

Answer 1

For this problem,all we have to do is translate the word problem into algebraic equations. The equations are as follows:

L = √100 * x = 10x
W = 1/2*y - 3/2*x

Since A is equal to length times width
A = LW
If L is given, we can find the x. Therefore, we must set the equation where the dependent variable is y and the independent variable is x.

125 = LW
W = 125/L
1/2*y - 3/2*x = 125/10x
10x(1/2*y - 3/2*x) = 125
5xy - 15x² = 125
xy - 3x² = 25
y = (25+3x²)/x
y = 25/x + 3x