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
Oct 2, 2015

Answer:

If we write #w# for the width in #"cm"#, then #w(w+3) = 70#.

Hence we find #w = 7# (discarding negative solution #w = -10#).

So width #= 7"cm"# and length #= 10"cm"#

Explanation:

Let #w# stand for the width in #"cm"#.

Then the length in #"cm"# is #w + 3# and the area in #"cm"^2# is #w(w+3)#

So:

#70 = w(w+3) = w^2+3w#

Subtract #70# from both ends to get:

#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 #70# which differ by #3#.

It should not take long to find #70 = 7 xx 10# fits the bill, hence we find:

#w^2+3w-70 = (w-7)(w+10)#

So #w^2+3w-70 = 0# has two solutions, viz #w = 7# and #w = -10#.

Since we're talking about lengths, we can ignore the negative solution leaving #w = 7#. That is the width is #7"cm"# and the length is #10"cm"#.