Question

The width of a rectangle is 6 inches less than it’s length, and the area is 7 square inches. What are the length and width of the rectangle

Answer 1

So length is 7 in while width is 1 in.

Explanation:

We are given W is 6 inches less than L which mean as an equation we have W=L-6.

We are given the area of this rectangle, LW=7.

So we have the system:

W=L-6

LW=7.

Replace the second W with what the first W equals:

LW=7

L(L-6)=7

Distribute:

`L^2-6L=7`

Subtract 7 on both sides:

`L^2-6L-7=0`

We are luck since the coefficient of L^2 is 1. This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.

Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.

So the factored form of our equation is:

(L-7)(L+1)=0

This gives us two equations to solve:

L-7=0 or L+1=0

L=7 or L=-1

L=-1 doesn't make sense for a length so L=7.

L=7 means the length is 7 inches.

If W=L-6 and L=7, then W=7-6=1.

The width is 1 inch since W=1.

So length is 7 in while width is 1 in.

Answer 2

W is the width, L is the length.
W=L-6) because the width is 6 less than the length. Since area is LxW, this is represented by 7= L(L-6)
So 7 = L^2-6L and then subtract 7 to get the quadratic equation L^2-6L-7
And this factors out to (L-7)(L+1): L=7,-1 but length can’t be negative so the length is 7. To find the width you do (7-6) which is 1, so the length is 7 and the width is 1.