422 algebra De mystif ieD
- The classroom’s length is 14 feet more than its width, so L = W + 14.
The diameter is 34 feet. The formula DL^22 = + W^2 becomes 34^2 =
(W + 14)^2 + W^2.
34 14
1156 14 14
1156 28 1
222
2
2
=++
=+ ++
=++
()
()()
WW
WW W
WW 996
1156 228 196
02 28 960
1
2
0 1
2
2
2
2
2
2
+
=++
=+−
=
W
WW
WW
() (W ++−
=+−
=− +
28 960
014 480
01630
2
W
WW
WW
)
()()
W − 16 = 0 W + 30 = 0 (This does not lead to a solution.)
W = 16
The classroom is 16 feet wide and 16 + 14 = 30 feet long.
We now work with other geometric shapes.
EXAMPLES
The area of a triangle is 40 in^2. Its height is four-fifths the length of its base.
What are its base and height?
The area is 40 and HB = ^45 so the formula AB = 21 H becomes 40 = ^12 BB() 54.
40 1
2
4
5
40 1
2
4
5
40 2
5
5
2
40
100
1
2
2
2
2
=
=⋅
=
⋅=
=
BB
B
B
B
B
00 =B
The triangle’s base is 10 inches long and its height is ()^45 (10) = 8 inches.
EXAMPLES
The area of a triangle is 40 in
What are its base and height?
EXAMPLES
The area of a triangle is 40 in