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

Answer:

2feet and 8 feet.

Step-by-step 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 $a=\frac{L*h}{2}$. Then:

$8=\frac{L(6+L)}{2}$

$8=\frac{6L+L^2)}{2}$

$16 = 6L+L^2$

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

we are going to use cuadratic formula to find L.

$L =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ where a= 1, b=6 and c=-16. Then,

$L =\frac{-6\pm\sqrt{36-4(1)(-16)}}{2}$

$L =\frac{-6\pm\sqrt{36+64}}{2}$

$L =\frac{-6\pm\sqrt{100}}{2}$

$L =\frac{-6\pm10}{2}$

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.

Answer 2

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.