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?

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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#