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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.

Respuesta :

tonb
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.
botellok

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 [tex]a=\frac{L*h}{2}[/tex]. Then:

[tex]8=\frac{L(6+L)}{2}[/tex]

[tex]8=\frac{6L+L^2)}{2}[/tex]

[tex]16 = 6L+L^2[/tex]

[tex]L^2+6L -16 = 0[/tex]

we are going to use cuadratic formula to find L.

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

[tex]L =\frac{-6\pm\sqrt{36-4(1)(-16)}}{2}[/tex]

[tex]L =\frac{-6\pm\sqrt{36+64}}{2}[/tex]

[tex]L =\frac{-6\pm\sqrt{100}}{2}[/tex]

[tex]L =\frac{-6\pm10}{2}[/tex]

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.

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