Question

The height of a triangle is 6 inches less than the base. The area of the triangle is 67.5 square inches. Find the length of the base and the height of the triangle.

Answer 1

Base: 15 Height: 9

Explanation:

Let's call the height of the triangle h, and the base b.

`h=b-6\\(bh)/(2)=67.5\\bh=135\\b(b-6)=135\\b^2-6b=135\\b^2-6b-135=0\\(b-15)(b+9)=0\\b=-9, 15`

Since the length of the side of a triangle cannot be negative, the length of the base is 15, and the height is 9. Hope this helps!