Chapter 8 linear appliCaTionS 303

So we now have the equation, with one unknown: (l + 3)^2 = l^2 + 33.

()

()()

(

ll

ll l

ll ll

+=+

++=+

++=+

333

33 33

69 33

22

2

(^222) oneeachsidecancels.)
−−

=

99
624
24
6
4
l
l
l
The original length is 4 cm.
The radius of a circle is increased by 3 cm. As a result, the area is increased
by 45π cm^2. What is the original radius?
Remember that the area of a circle is A = or^2 , where r represents the radius.
So, let r represent the original radius. The new radius is then represented
by r + 3. The new area is represented by o(r + 3)^2. But the new area is also
the original area plus 45o cm^2. This gives us A + 45o = o(r + 3)^2. Because A =
or^2 , A + 45o becomes or^2 + 45o. Our equation, then, is or^2 + 45o = o(r + 3)^2.
or^2 + 45o = o(r + 3)^2
or^2 + 45o = o(r + 3)(r + 3)
or^2 + 45o = o(r^2 + 3r + 3r + 9)
or^2 + 45o = o(r^2 + 6r + 9)
or^2 + 45o = or^2 + 6ro + 9o (or^2 on each side cancels.)
45 o = 6ro + 9o
–9o –9o
36 o = 6ro
36
6
o
o
 = r
6 = r
The original radius is 6 cm.
PRACTICE

1. A rectangular piece of cardboard starts out with its width being three-
   fourths its length. Four inches are cut off its length and 2 inches from its

PRACTICE

1. A rectangular piece of cardboard starts out with its width being three-