SOLUTION: A side of a triangle is 4 meters shorter than the hypotenuse. The other side is 8 meters shorter than the hypotenuse.Find the area of the triangle. Please help me huhuhu asap p

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Question 981220: A side of a triangle is 4 meters shorter than the hypotenuse. The other side is 8 meters shorter than the hypotenuse.Find the area of the triangle.
Please help me huhuhu asap pls im begging thank you so much
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
Hi there,
First of all you must solve for
the hypotenuse.
If you make the hypotenuse = x
Side = x - 4
Other side = x - 8
Using Pythagoras
(x - 4)^2 + (x - 8)^2 = x^2
Multiplying out
(x^2 - 8x + 16)+(x^2 - 16x + 64) = x^2
Removing brackets and collecting like terms
2x^2 - 24x + 80 = x^2
x^2 - 24x + 80 = 0
Factorise
(x - 4)(x - 20)= 0
x - 4 = 0
x = 4 (No value as x -4 = 0
......and x - 8 = -4
x - 20 = 0
x = 20
This gives the sides a value of
x - 4 = 16
x - 8 = 12
Hypotenuse = 20
A 3:4:5 triangle
Area = 1/2 (base X height)
Area = 1/2 (16 X 12)
Area = 1/2(192)
Area = 96m^2
Hope this helps:-)