A rectangular ink pad has a perimeter of 30 centimeters. Its area is 54 square centimeters. What are

Do you know what the words mean? That is the first step in solving a word problem.

Say the sides are X and Y. Then perimeter P = 2X + 2Y and area A = XY.

So you are given
54 = XY

and
30 = 2X + 2Y The rule is you can do any valid operation on both sides of an equation and it will still be equal. Divide by 2.

15 = X + Y Subtract Y and rewrite.

X = 15 - Y Now substitute this for X in the other equation.

54 = (15 - Y)Y

54 = 15Y - Y^2 Subtract the entire right side.

Y^2 - 15Y + 54 = 0

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem

So we want to find something of the form (Y + a)(Y + b) = 0 and a + b = -15. So we examine factors of 54. The first one we try is 3 x 18 = 54 and we notice that 3 - 18 = -54.

(Y + 3)(Y - 18) = 0

Y = -3 and X = 18

or Y = 18 and X = -3

The signs mean that you can measure Y up, positive, or down, negative, and X can be right, positive, or left, negative.