bob wants to build a doghouse that is 2 feet longer than it is wide. he's building it on a concrete slab that will leave 2 feet of concrete slab visible on each side. if the area of the doghouse is 48 square feet, what are the dimensions of the concrete slab

10 ft by 12 ft

Step-by-step explanation:

This problem requires you to first write an equation to represent the situation. Here we will represent the shorter side of the doghouse with the variable x, the longer side will be represented with x+2 because it is 2 feet longer.

48 = x * (x+2)

This represents the area of the doghouse as the product of the width and length of the doghouse.

48 = x^2 + 2x

Now, we need to move all the items onto one side of the equals sign, it is best to have the x^2 be positive.

0 = x^2 + 2x - 48

Now, we factor to find what x equals.

0 = (x-6) * (x+8)

From here, we can use each of the terms in parentheses to solve for x.

0 = x-6

x = 6

0 = x+8

0 = -8

Here we know that the shorter side has to be 6 ft because length is a positive number, and we can determine that the longer side is 8 ft because it is 2 ft longer. The dimensions of the slab are therefore 10 ft by 12 ft because the slab is 2 ft on each side, therefore adding an extra 4ft to the dimensions because the 2ft is added on each side.