If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

Question

3640 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T16:18:54

The length is 20 cm and the width is 15 cm

First, let's call the width of our rectangle #w# and the length #l#.

From the problem we know:

#w = 1/2l + 5#

We also know the formula for the perimeter of a rectangle is:

#p = 2*l + 2*w#

So we can substitute #70# for #p# which is given in the problem and we can also substitute #1/2l + 5# for #w# and then solve for #l#:

#70 = 2*l + 2*(1/2l + 5)#

#70 = 2l + 1l + 10#

#70 = 3l + 10#

#70 - 10 = 3l + 10 - 10#

#60 = 3l#

#60/3 = (3l)/3#

#20 = l#

Now we can substitute #20# for #l# in the formula for #w# to find the width:

#w = 1/2 20 + 5#

#w = 10 + 5#

#w = 15#