SOLUTION: I need help i don't know how to solve Problem Solving like this :(
The base of an isosceles triangle is 8 m more than its altitude. If its area is 192 m^2, find the length of its
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The base of an isosceles triangle is 8 m more than its altitude. If its area is 192 m^2, find the length of its
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Question 1044784: I need help i don't know how to solve Problem Solving like this :(
The base of an isosceles triangle is 8 m more than its altitude. If its area is 192 m^2, find the length of its sides. Found 2 solutions by Alan3354, Cromlix:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! I need help i don't know how to solve Problem Solving like this :(
The base of an isosceles triangle is 8 m more than its altitude. If its area is 192 m^2, find the length of its sides.
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Area = b*h/2 = 192
b*h = 384
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Find a pair of factors of 384 that differ by 8
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b = 24
h = 16
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The altitude forms 2 right triangles with sides of 12 & 16
The 2 equal sides are sqrt(12^2 + 16^2) = 20
--> sides are 20, 20 & 24
You can put this solution on YOUR website! Hi there,
Area of a triangle is = 1/2(base x height)
Make height (altitude) = x
Base = x + 8
Area = 1/2(base x altitude)
192 = 1/2(x(x + 8))
192 = 1/2(x^2 + 8x)
Multiply both sides by 2
384 = x^2 + 8x
Rearrange into ax^2 + bx + c form
x^2 + 8x - 384 = 0
Factorise
(x - 16)(x + 24) = 0
x + 24 = x = -24 (discount as -ve)
x - 16 = 0
x = 16
Altitude = 16 m
Base = 24 m
........
Now we can work out the size of the two
equal sides by dividing the base of 24 m
into 2 lots of 12 m.
We now have a right angled triangle
with base of 12 m and an upright of
16 m.
To find the hypotenuse we use Pythagoras' Theorem.
Namely:- Hypotenuse^2 = 12^2 + 16^2
Hypotenuse = √144 + 256
Hypotenuse = √400
Hypotenuse = 20 m
.............
Two equal sides = 20 m
Base = 24 m
Hope this helps :-)
