Question

The height of a triangle is 4 inches greater than the base. The area of the triangle is 70 square inches.

Answer 1

Answer: 10 inches.

Step-by-step explanation:

We have to solve a system of equations.

The formula to calculate a triangle area is A = (b.h)/2

where b is the base and h is the height. This will be our first equation.

Since the height is 4 inches greater than the base, the second equation will be: h = b+4

We replace h and the value of the area (70 square inches) in the first equation, and we solve it by using the cuadratic equation formula:

70 = (b . (b+4)) / 2

70 . 2 = b² + 4b

140 = b² +4b

0 = b² + 4b - 140

The roots of this polynomial are -14 and 10. Since a distance can't be negative, the length of the base is 10 inches.