# 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