The length of a rectangle is 3 cm more than the width. The area is 70cm^2. How do you find the dimensions of the rectangle?
1 Answer
If we write
Hence we find
So width
Explanation:
Let
Then the length in
So:
#70 = w(w+3) = w^2+3w#
Subtract
#w^2+3w-70 = 0#
There are a variety of ways to solve this, including the quadratic formula, but we can instead recognise that we're looking for a pair of factors of
It should not take long to find
#w^2+3w-70 = (w-7)(w+10)#
So
Since we're talking about lengths, we can ignore the negative solution leaving