The height of a triangle is 7 inches less than 5 times the length of its base. The area is 26 square inches. Find the length (in inches) of the base and the height (in inches) of the triangle.

Answer 1

h=5b-7

A=26 = hb/2 = (5b-7)b/2

5b^2 -7b = 52

5b^2 -7b -52 = 0

(5b+13)(b-4) = 0 ignore the negative solution -13/5

b-4 = 0

b=4 inches = base length

h =5(4)-7= 13 inches high

4x13/2 = 26 in^2 area