A rectangle has an area of 156 square inches and a perimeter of 50 inches. Which could be the length and width of the rectangle?

Answer 1

The area of the rectangle = l x w = 156

The perimeter is 2l+2w = 50

2(l+w)= 50

l+w = 50/2

l = 25 - w

Therefore

lxw = 156

(25-w) x w = 156

25w -w² =156

Therefore w²-25w +156 = 0

Using the quadratic formula for ax² +bx +c

where  

we get w = (-(-25) + or - (square root of (-25)² -4(1)(156))) all over 2(1)

= ( 25 + or - (square root of (625-624)) all over 2

= (25 + or - (square root of 1) all over 2

= (25 + or - 1) all over 2

= 26/2 or 24/2

= 13 or 12 (You can use either or)

i = 25 - w

l = 25 - 13 = 12

Thus l = 12 and w = 13 could be the length and width of the rectangle giving us l x w = 156 and 2l +2w = 50.