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.