Question 262079: how do you find the length and width of a triangle using the area? the area is 39 cm and the lenght is 7cm greater than the height.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! how do you find the length and width of a triangle using the area? the area is 39 cm and the length is 7cm greater than the height.
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generally with a triangle, you refer to the dimensions as the base(b) & the height(h)
:
.5*b*h = area (39 sq/cm in this case)
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In this triangle,"the base is 7 cm greater than the height", so we can say
b = (h+7)
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Substitute (h+7) for b in the area equation and find h
.5*(h+7)*h = 39
.5(h^2 + 7h) = 39
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Get rid of the decimal .5, multiply both sides by 2
h^2 + 7h = 2(39)
h^2 + 7h = 78
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Arrange as a quadratic equation
h^2 + 7h - 78 = 0
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This will factor to
(h + 13)(h - 6) = 0
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then positive solution is what we want here
h = 6 cm is the height
then
b = h + 7
b = 6 + 7
b = 13 cm is the base
;
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Check this by finding the area
.5*13*6 = 39
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