Algebra help! (1 Viewer)

big_bang344 · Sep 11, 2011

In a right angled triangle, the hypotenuse is 8cm longer than the shortest side and 1 cm longer than the third side. Find the length of the third side.

Can anyone help me with this. Tried so many times but can't get the answer.

big_bang344 · Sep 11, 2011

Oh, and actually show me how you did it. Thanks!

AAEldar · Sep 11, 2011

Let length of the hypotenuse be x, length of the shortest side be x-8 and length of the third side be x-1. Apply Pythagoras:

$x^2=(x-1)^2+(x-8)^2 \\ x^2=x^2-3x+1+x^2-16x+64 \\ x^2-18x+65=0 \\ (x-5)(x-13)=0 \\ \therefore x=13\text{ since }5-8\text{ is negative, and }x\text{ must be greater than zero.} \\ \text{Hence length of third side is 12cm.}$

big_bang344 · Sep 11, 2011

Woah. Thanks Eldar.

SpiralFlex · Sep 11, 2011

big_bang344 said:
Woah. Thanks Eldar.

You shall address him as Sir Eldar.

AAEldar · Sep 11, 2011

big_bang344 said:
Woah. Thanks Eldar.

Haha no worries. Hopefully it makes sense

SpiralFlex said:
You shall address him as Sir Eldar.

Thought that was only reserved for you?

Algebra help! (1 Viewer)

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