Find the dimensions of a rectangle whose area is 209 cm2 and whose perimeter is 60 cm.

Question

College algebra hw help

Answer 1

If the dimensions are a and b, then ab=area=209 and 2(a+b)=60, so a+b=30 and b=30-a.

So we substitute for b in the area: a(30-a)=209.

30a-a²-209=0 or in standard form a²-30a+209=0.

We are looking for factors of 209 that differ add up to 30: 11 and 99 are the only integer factors of 209 and they happen to add up to 30, so: (a-11)(a-19)=0 and whichever value we use for a, b=30-a so we end up with 11 and 19 as the dimensions in centimetres.