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The length and width of a rectangle are consecutive integers. The area of the rectangle is 156 square feet. Find the length and width of the rectangle.​

User Afitnerd
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1 Answer

4 votes

Answer:

L = 12ft

W = 13ft

Explanation:

Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).

The length and width are consecutive integers

L+1=W

The area of the rectangle is 156 square feet.

L*W=156

We know that W=L+1 from our first equation, so substituting that information into our second equation we get

L*(L+1)=156

Let's distribute that L

L^2 + L = 156

and subtract 156 from both sides

L^2 + L - 156 = 0

Now we can use the quadratic formula to find L. L cannot be negative, so

L = 12

using our very first equation we know L, so we can solve for W.

L+1=W

12+1=W

W = 13

User Npr
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