Find the dimensions of the rectangle

Question

The length of a rectangle is 4cm more than the width the area is 96cm² 

Answer 1

In this problem we have the length (l) and the area (A) of a triangle. The length is 4 more than the width. we can have the width be represented by w. Therefore, if the length of the triangle is 4 more than the width, the length would be: w + 4.

 

The equation for finding the area of a rectangle is: A = lw

 

If if I fill out the equation with our filler values, we get: 96cm² = (w+4)(w). Then you solve - 

 

96cm² = (w+4)(w)

96 = w² + 4w

0 = w² + 4w - 96

 

Oh hey, quadratic equation! First we need to separate it into two parts.

0 = (w +   )(w -   ) Cool. Now we need two numbers whose product = 96, and whose difference = 4.

0 = (w + 12)(w - 8) Awesome. Now set each side equal to 0 and solve. Why? Because anything times 0 equals 0. Therefore, the equation will be true as long as one of those two parts is equal to 0.

 

w + 12 = 0

w = -12

 

w - 8 = 0

w = 8

 

w = -12 ; w = 8. Only one of these answers is possible for a measurements. You can't have negative length measurements because then you're traveling into other dimensions. And if you are, please take picture, that is groundbreaking science.

 

So there's the width! w = 8. So what's the length again? Oh right 4 more than the width.

 

l = 12 and w = 8.