Question

The sides of rectangle x are each multiplied by a to form rectangle y and by b to form rectangle z. A times the area of x is 10, and b times the area of x is 5. If the difference in area between y and z is 300, what is a - b?

Answer 1

Set sides of rectangle X are L and W

Area of X: = LW Area of Y = (aL)(aW) = a^2 * LW Area of Z = (bL)(bW) = b^2 * LW a times area X = aLW = 10 b times area X = bLW = 5

Which means that difference between Y and Z = aaLW – bbLW = 300.

And since you're looking to solve for a - b, you can try to get a and b alone by factoring out the common LW terms:

LW(a^2 - b^2) = 300

Which gives you the Difference of Squares setup that allows you to get (a - b) alone:

LW(a + b)(a - b) = 300

Then you should see that if you distribute LW across the first set of parentheses, you can get aLW and bLW, for which you have actual values:

(aLW + bLW)(a - b) = 300

(10 + 5)(a - b) = 300 15(a - b) = 300 (a - b) = 20