426 algebra De mystif ieD
✔SOLUTIONS
- The area formula for a triangle is AB = ^12 H. The area is 12. The length of
its base is two-thirds its height, so BH = ^23. The formula becomes
12 1
2
2
3 = HH
.12 1
22
3
12 1
22
3
12 1
3
312
36
6222
2=
=⋅==
=
=HHHHH
H()HHThe height of the triangle is 6 inches. Its base is ()^2364 = inches.- The formula for the area of a triangle is AB = 21 H. The area is 20. The
height is 3 cm more than the base, so H = B + 3. The formula becomes
20 (= 21 BB )+ 3.
20 1
23
2203
40 3
40 3
032
2=+
=+
=+
=+
=+BB
BB
BB
BB
BB()
() ()
()−−
=− +40
05 ()()BB 8B − 5 = 0 B + 8 = 0 (This does not lead to a solution.)
B = 5
The triangle’s base is 5 cm and its height is 5 + 3 = 8 cm.- The formula for the area of a triangle is AB = 21 H. The area is 20. The
equation B + H = 14 gives us so H = 14 − B. The formula becomes
20 (= 21 BB 14 )– .