the length of a rectangle is 8 feet more than its width. the area of the rectangle is 84 square feet. find its length and width

Question

Solving equations by factoring

Answer 1

Hi Samantha,

 

You can start by drawing a diagram.  Then, you need to pick the shorter side and designate it as "x".  The longer side must be "x+8".

 

The formula for area of a rectangle is A=l*w.  Since the area is 84, then you can use the A=l*w formula.  84 = x(x+8) would be the equation to solve for x.

 

Now, you need to put the equation in standard form.  So, x² + 8x - 84 = 0.

 

Since you can't solve this quadratic using factoring, you need to complete the square.

 

To complete the square you need to add 84 to both sides.  Now you have x² + 8x = 84.  Take the coefficient for the x term (8) and divide by 2.  Now square it.  That would be 4², so 16.  Now you have x² +8x +16 = 100.

 

Factor x² +8x +16, so (x+4)² = 100

 

If you use the square root property, you have x+4 = 10.  Therefore, x = 6 (the short side) and 14 is the long side.

 

I hope that helps.

Dr. V