The length of a picture frame is 8in less than 3 times its width ding the length and width of the area is 60 inches square

Question

Help please

Answer 1

Here's what we know:

A = lw

l = 3w - 8

A = 60

so we have:

60 = w(3w - 8)

60 = 3w2 - 8w

0 = 3w2 - 8w - 60

 

I'm going to use the quadratic formula here to find w:

(-b  ± √(b² - 4ac)) / 2a

 

(-(-8) ± √((-8)² - 4 * 3 * -60)) / (2 * 3)

(8 ± √(64 - 4 * 3 * -60)) / 6

(8 ± √(64 + 720)) / 6

(8 ± √784) / 6

(8 ± 28) / 6

So we have 36 / 6 and -20/6. Since we can't have a negative for an area, we're left with 36/6 which is 6

 

l = 3 * 6 - 8

l - 18 - 8

l = 10

check:

60 = A = 10 * 6

60 =  60