SOLUTION: A section on the playground is in the shape of a triangle and has an area of 24 square feet. If the base is four more than twice the height, what is the measure of the height?

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Question 885365: A section on the playground is in the shape of a triangle and has an area of 24 square feet. If the base is four more than twice the height, what is the measure of the height?

Found 3 solutions by nerdybill, Theo, dkppathak:
Answer by nerdybill(7384)   (Show Source):
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A section on the playground is in the shape of a triangle and has an area of 24 square feet. If the base is four more than twice the height, what is the measure of the height?
Let h = measure of height
then
4+2h = measure of base
.
area of any triangle is (1/2)base*height
(1/2)(4+2h)h = 24
(2+h)h = 24
2h+h^2 = 24
h^2+2h-24 = 0
(h+6)(h-4) = 0
h = {-6, 4}
throw out the negative solution (extraneous) leaving:
h = 4 feet

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
area of a triangle is equal to 1/2 * base * height.
area = 24
base = 4 * height.
formula of area = 1/2 * base * height becomes:
area = 1/2 * 4 * height * height which becomes:
24 = 2 * height squared which becomes:
12 = height squared which becomes height = square root of 12.
you have:
area = 24
base = 4 * sqrt(12)
height = sqrt(12)
area = 1/2 * base * height = 1/2 * 4 * sqrt(12) * sqrt(12) = 1/2 * 4 * 12 = 2 * 12 = 24.
numbers check out.
base = 4 * sqrt(12)
height = sqrt(12)

Answer by dkppathak(439)   (Show Source):
You can put this solution on YOUR website!
A section on the playground is in the shape of a triangle and has an area of 24 square feet. If the base is four more than twice the height, what is the measure of the height?
Solution
as per given conditions base is four more than twice the height,
base =2 x height +4 let base is b and height is h
Area of triangle = 1/2(base x height)
24 =1/2(2h+4)h by cross multiplication
48=(2h+4)h
48 =2h^2+4h take 2 common
24 =h^2+2h
h^2+2h-24=0 by factorization spiting middle term
h^2+6h-4h-24=0
(h+6)(h-4)=0
h=-6 or h=4 neglecting negative 6 value
so height =4 feet
base = 12 feet
answer