Need help please!!! thanks!!!

Question

The base of a triangle is 3 meters longer than the height of the triangle. If the area of the triangle is 44 square meters, what are the base and height of the triangle?

 

 

The height is ___ meters

 

The base is ___ meters

Answer 1

Area of triangle = 1/2 (base * height)

 

base is 3 meters longer than the height, so base = height + 3

 

Substitute base by height +3 in the equation for area of the triangle and solve the equation for height.

 

Answer 2

The area of a triangle can be expressed as A = 1/2bh, where "A" is the area, "b" is the base, and "h" is the height.

 

According the information given in the problem, b = h + 3, and the area of the triangle is 44 m^2

 

Let's plug this into our equation:

 

A = 1/2bh

44 = 1/2(h + 3)(h)

44 = 1/2(h^2 + 3h)

44 = 1/2h^2 + 3/2h

0 = 1/2h^2 + 3/2h - 44

 

To make the math easier, I'm going to multiply the equation by 2

 

0 = h^2 + 3h - 88

 

Factor and solve

 

0 = (h + 11) (h - 8)

 

h + 11 = 0

h = -11

 

h - 8 = 0

h = 8

 

 

 

Because a distance cannot be a negative number, h must equal 8.

 

Therefore, the height is 8 meters, and the base is 11 meters.