Chapter 11 QuaDraTiC appliCaTionS 427
20
1
2
14
40 14
40 14
01440
0
2
2
=−
=−
=−
=−−
−=
BB
BB
BB
BB
()
()
()−−−−
=− ++
=− +
=− −
()
()(
14 40
01440
01440
010
2
2
2
BB
BB
BB
BB 4 4)
B − 10 = 0 B − 4 = 0
B = 10 B = 4
There are two triangles that satisfy the conditions. If the base is
10 inches, the height is 14 − 10 = 4 inches. If the base is 4 inches, the
height is 14 − 4 = 10 inches.
- By the Pythagorean theorem, a^2 + b^2 = c^2. The hypotenuse is c, so c = 85.
One leg is 71 longer than the other so a = b + 71 (b = a + 71 also works).
The Pythagorean theorem becomes 85^2 = (b + 71)^2 + b^2.
85 71
7225 71 71
7225 142
222
2
2
=+ +
=+ ++
=+ +
()
()()
bb
bbb
bb 55041
7225 2 142 5041
02 142 2184
1
2
0
2
2
2
+
=++
=+ −
=
b
bb
bb
()^11
2
2 142 2184
071 1092
01384
2
2
()
()()
bb
bb
bb
+−
=+−
=− +
b − 13 = 0 b + 84 = 0 (This does not lead to a solution.)
b = 13
The shorter leg is 13 cm and the longer leg is 13 + 71 = 84 cm.