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 1222
2
2=++
=+ ++
=++()
()()WW
WW W
WW 996
1156 228 196
02 28 960
1
20 1
222
2
22+
=++
=+−
=W
WW
WW
() (W ++−=+−
=− +28 960014 480
016302WWW
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
24
5
40 1
24
5
40 2
5
5
240100
12222=
=⋅=⋅==BBBBBB
00 =BThe 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