Question 790401: An area for the press was supposed to be shaped as an equilateral triangle with a fence around it. Unfortunately Mr Spendalot's nephew was put in charge of this and he didn't know how to measure. He seems to have put 3 metres less on one side, an extra four metres onto another side that wasn't supposed to be there and the longest side now has double the amount of fencing on it than it was supposed to.
To Mr Spendalot dismay the triangle was a much less pleasing right angled triangle now and has to be quickly changed back.
By drawing the new triangle and using Pythagoras' theorem find the dimensions of the original triangle to the nearest cm.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An area for the press was supposed to be shaped as an equilateral triangle with a fence around it.
Unfortunately Mr Spendalot's nephew was put in charge of this and he didn't know how to measure.
He seems to have put 3 metres less on one side, an extra four metres onto another side that wasn't supposed to be there and the longest side now has double the amount of fencing on it than it was supposed to.
To Mr Spendalot dismay the triangle was a much less pleasing right angled triangle now and has to be quickly changed back.
By drawing the new triangle and using Pythagoras' theorem find the dimensions of the original triangle to the nearest cm.
:
let s = the side of the required equilateral triangle
then
(s-3) = the shorter leg of the right triangle
(s+4) = longer leg of the right triangle
2s = the hypotenuse
:
using pythag
(s-3)^2 + (s+4)^2 = (2s)^2
FOIL
s^2 - 6s + 9 + s^2 + 8s + 16 = 4s^2
Arrange as a quadratic equation on the right
0 = 4s^2 - s^2 - s^2 + 6s - 8s - 9 - 16
2s^2 - 2s - 25 = 0
Use the quadratic formula, I got a positive solution of
s = 4.0707 is the side of the equilateral they want. (4m 7cm)
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