The base of a triangle is 3 meters longer than the height of the triangle. If the area of the triangle is 14 square meters, what are the base and height of the triangle?

Question

The base of a triangle is 3 meters longer than the height of the triangle. If the area of the triangle is 14 square meters, what are the base and height of the triangle?

Answer 1

Let b be the base and h be the height

b = h + 3

area of a triangle = bh/2 = 14 -> h = 28/b

So, b = 28/b + 3 --> b² = 28 + 3b

Or

b² -3b -28 = 0 -> (b-7)(b+4) = 0 , so b = 7, -4

Take the positive one since it is a length

b = 7 and h=28/7 = 4

Answer 2

Hi Michelle C.

You can set up a quadratic equation here with the information given

Area = 1/2(bh)

b = h + 3

14 = h(h + 3)/2

Multiply both sides of the equation by 2

28 = h² + 3h

Subtract 28 from both sides to yield a quadratic

0 = h² + 3h -28

Factor the quadratic

0 = (h + 7)(h -4)

h = 4 is the only solution since h cannot be negative

Substitute h into the equation b = h + 3 to find the base

b = h + 3 = 4 + 3 = 7

h = 4

b = 7

You can check this by calculating the Area

1/2(bh) = 14

1/2(7*4) = 14

1/2(28) = 14

14 = 14