Question

The area of a triangle is 16 square units. The base of the triangle is four more than the height of the triangle. What is the base and height of the triangle?

Answer 1

To solve for the base and height with a given area of 16 square units and the base being four more than the height, we use the area formula for a triangle and quadratic factoring, finding that the base is 8 units and the height is 4 units.

Step-by-step explanation:

To find the base and height of a triangle when given the area and a relationship between the base and height, we can use the area formula for a triangle, which is Area = 1/2 × base × height. Since the area is given as 16 square units and the base is said to be four more than the height, let's denote the height as h and the base as h + 4. Substituting these into the area formula, we get:

16 = 1/2 × (h + 4) × h

Multiplying both sides by 2 to get rid of the fraction, we obtain:
32 = (h + 4) × h. Now, we can expand this to create a quadratic equation: h² + 4h - 32 = 0. This can be factored into (h + 8)(h - 4) = 0, giving us two possible solutions for h: -8 and 4. Since negative height is not possible for a triangle, we discard -8 and take h = 4 as the height. Therefore, the base is h + 4 = 4 + 4 = 8 units.

The base of the triangle is 8 units and the height is 4 units.

Answer 2

let x=height. then base is x+4. plug what we know into the formula for the area of a triangle

A=½bh

16=½*(x+4)*(x)

32=x²+4x

x²+4x-32=0
(x+8)(x-4)=0
so x can be-8 our 4. when we plug-8 in for x we get a negative height. since a triangle cannot have a negative side length we discard-8 and try 4. height=4 and base=8