A triangle with an area of 476 square inches has a height that is 16 less than 6 times its base. Find the base and height, in inches, of the triangle.

Answer 1

B = base

H = 6B - 16

area = 1/2 (base)(height)

1/2*B*(6B-16)

476 = 1/2*B*(6B-16)

476 = 3B^2 - 8B

3B^2 - 8B - 476 = 0

use quadratic formula

B = -b +/- sqrt(b^2-4ac)

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2a

where a = 3, b = -8 and c = -476

solutions will be 14 and -11.33, of which only 14 is the viable solution.

so B = 14 and H = 6B - 16 = 6*14 - 16 = 68

check:

1/2 * 14 * 68 = 476

Answer 2

Let b = base and h = height

Area = 1/2 *b*h

h = 6b -16

Area = 476

Then, 476 = 1/2 * b *(6b - 16)

476 = 3b^2 - 8b

3b^2 - 8b - 476 = 0

Solve this equation we get b = 14

So, h = 6*14 - 16 = 68

Base = 14 and height = 68