Question

The height of a triangular flower garden is 6 feet more than the length of the base. If the area of the garden is 8 square feet, find the dimensions of the flower garden.

Answer 1

From the text you can derive the following equations:

(1) A = bh/2 = 8
(2) and h = b+6

Fill in h in (1):

b(b+6)/2 = 8 => b^2 + 6b = 16 with the quadratic formula or simply trying some values for b you can find b=2, so h=8.

Answer 2

2feet and 8 feet.

Explanation:

Let's call L to the length of the garden. Now, we have that the height h is

h = 6+L and the area of a triangle is
`a=(L*h)/(2)`. Then:

`8=(L(6+L))/(2)`

`8=(6L+L^2))/(2)`

`16 = 6L+L^2`

`L^2+6L -16 = 0`

we are going to use cuadratic formula to find L.

`L =(-b\pm√(b^2-4ac))/(2a)` where a= 1, b=6 and c=-16. Then,

`L =(-6\pm√(36-4(1)(-16)))/(2)`

`L =(-6\pm√(36+64))/(2)`

`L =(-6\pm√(100))/(2)`

`L =(-6\pm10)/(2)`

So, L = 4/2 = 2 or L = -16/2 = -8 but as we are searching lengths, we use the positive result. Then L = 2. Finally we have that the length of the triangle is 2 feet and the height is 2+6 = 8 feet.