The parameter of PQRS equals 84 therefore what is the length of each side if PS=RSsquared

Question

The parameter of PQRS equals 84.  What is the length of each side given the following conditions:

SP=RS2(squared)

Answer 1

I will assume we have a rectangle here, since you did not specify.

In that case, we have:

SP = RQ
RS = PQ
SP = (RS)^2

Let SP = x. Thus, RQ = x, RS = x^2 and SP = x^2.

The perimeter of the rectangle is 84, so we have:

x + x + x^2 + x^2 = 84
2x^2 + 2x - 84 = 0
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0
x = -7 or x = 6

We reject x = -7, since hte length cannot possibly be negative.
Thus, x = 6.

Hence, the length for each side is:

SP = 6^2 = 36
RS = 6^2 = 36
RQ = x = 6
SP = x = 6