SOLUTION: If the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. If the altitude is increased by 3 inches a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. If the altitude is increased by 3 inches a      Log On


   

Question 908978: If the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. If the altitude is increased by 3 inches and the base decreased by 2 inches the area will be increased by 5 square inches. Find the base and the altitude of the triangle.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
((b-2)(a+3) = ab + 10
ab -2a + 3b - 6 = ab + 10
-2a + 3b = 16
b = %2816%2B2a%29%2F3
(1/2)(b+4)(a+4) = (1/2)ab + 42
(b+4)(a+4) = ab + 84
ab + 4a + 4b + 16 = ab + 84
4a + 4b = 68 Substitute for b to find a
4a + 4%2816%2B2a%29%2F3 = 68
12a + 4(16+2a) = 204
20a = 140
a = 7 and b = 10 %2816%2B2%2A7%29%2F3