Word Problem (Factoring)

Question

A square piece of fabric has an area of 16x²+40x+25 square inches. The side lengths of the fabric can be found by factoring the area. Find an expression for the perimeter of the piece of fabric. Then find the perimeter when x=2.

Answer 1

The problem gives you a hint: it's a square piece of fabric. That means we're looking at square values again, and if we look at the a and c values we do indeed have squares here: 16 is 4², an 25 is 5².

So when we factor, a good starting point would be to look at the square roots of 16 and 25 as our factoring point:

(4x + 5)(4x + 5)

 

Let's check by multiplying that back out:

4x * 4x = 16x²

4x * 5 = 20x

5 * 4x = 20x

5 * 5 = 25

Combine like terms:

20x + 20x = 40x

 

So when FOILed back out, we get:

16x² + 40x + 25

 

Now for x = 2:

A = l*w

P = 2l + 2w

 

A = (4*2 + 5)²

 

P = 2(4*2 + 5) + 2(4*2 + 5) or just 4(4*2 + 5)

4(8+5)

P = 4(13)

P = 52

So the perimeter is 52 inches long

Answer 2

16x² + 40x + 25 =

(4x + 5)²

 

Length of side = 4x + 5

 

If x = 2,

perimeter = 4(4(2) + 5) = 4(8 + 5) = 4(13) = 52