SOLUTION: Help Needed Thank You! 1. One side of a right-angled triangle is 7cm longer than the other side and hypotenuse is 4cm less than the sum of the other two sides. i. Draw a diag

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Help Needed Thank You! 1. One side of a right-angled triangle is 7cm longer than the other side and hypotenuse is 4cm less than the sum of the other two sides. i. Draw a diag      Log On

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Question 1070786: Help Needed Thank You!
1. One side of a right-angled triangle is 7cm longer than the other side and hypotenuse is 4cm less than the sum of the other two sides.
i. Draw a diagram representing this information.
ii. Using Pythagoras' Theorem, form an equation representing the relationship between the three sides of the triangle. (Leave your answer in the simples form)
iii. Find the length of the shortest side.
Thank you so much if you answer this. I really appreciate it!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28x%2B7%29%5E2=%28x%2Bx%2B7-4%29%5E2
x%5E2%2B%28x%5E2%2B14x%2B49%29=%282x%2B3%29%5E2
2x%5E2%2B14x%2B49=4x%5E2%2B12x%2B9
2x%5E2-2x-40=0
x%5E2-x-20=0
%28x-5%29%28x%2B4%29=0
Two solutions but only one is positive,
x-5=0
x=5
The shortest side is xcm long, so the shortest side is 5 cm.