SEARCH HOME
Math CentralQuandaries & Queries

search

Question from bill, a student:

The area of the rectangle is 170 sq.ft. the width is unknown and the length is the width plus 7 ft.
I set it up like this w(w+7)=170 and this is where I get lost. Thanks, Bill

Hi Bill,

With w(w + 7) = 170 the next step should be to expand the left side. Using the dissimulative law

w(w + 7) = w × w + w × 7 = w2 + 7w

Hence you have

w2 + 7w = 170

Next subtract 170 from each side

w2 + 7w - 170 = 170 - 170
w2 + 7w - 170 = 0.

The task now is to factor w2 + 7w - 170, that is to find numbers a and b so that

w2 + 7w - 170 = (x + a)(x + b)

Notice that if you expand the right side you get

(x + a)(x + b) = x2 + (a + b)x + ab

Hence to have

w2 + 7w - 170 = (x + a)(x + b) = x2 + (a + b)x + ab

you want numbers a and b so that ab = 170 (so one is positive and one is negative) and a + b = 7.

Can you find a and b and complete the problem?

If you need further assistance write back,
Penny

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS