Question

LMNP is a rectangle. If LN = 9x – 14 and MP = 7x + 4, find the values of x, LN, and MP.

Answer 1

I am thinking of a rectangle that has the two sides parallel to one another. Set the two functions equal to one another, so

9x-14=7x+4

After a bunch of algebra and math magic, 2x=18 => x=9

So if you just insert 9 into both equations, both will end up with a value of 67, so it ends up looking like a right triangle. Don't do that. Instead, to find the rectangle widths, use 9x-4 (+10 added to intercept) instead, while keeping 7x+4, so that the intercepts match.

LN) 9x-4 = 9(9)-4 = 81-4 = 77
MP) 7(9)+4 = 63+4 = 67

*If you are also looking for the diagonals, use Pythagorean Theorem 77^2+67^2=(hypotenuse)^2*