Question

The length of a rectangle is one inch less than there times it’s width, if the perimeter is 54inches find the length

Answer 1

l = the width

L = the length

we translate the statement: L = l²-1

perimeter = 2(L+l) = 2(l²-1+l)= 2l²-2+2l= l²+l-1

perimeter = 54 simplified by 2 = 27

l²+l-1=27

l²+l-1-27=0

l²-l-28=0

b²-4ac = 1²-4(1*-28)=1+112=113

Δ = 113

(-b-√Δ)/2a =(-1-√113)/2≈-5.8150...

(-b+√Δ/2a =(-1+√113)/2≈4.8150...=4.8inches

the width = 4.8 inches

the length = 4.82²-1≈22.2321..=22.2inches

we check:

P=2(4.8+22.2)=54inches