Question

a rectangle has the length of 6 less than 4 times the width, of the perimeter of a rectangle is 176 inches, what is the numerical length of the rectangle

Answer 1

Let
`l,w` be the length and width of the rectangle, respectively.

On the one hand, we know that
`l = 4w-6`

On the other hand, we know that

`2(l+w)=176`

If we substitute the expression for l, we have

`2(4w-6+w)=176 \iff 5w-6 = 88 \iff 5w = 94 \iff w = (94)/(5)`

And we can deduce

`l = 4\cdot(94)/(5)-6 = (346)/(5)`