Each diagram below shows a right triangle with the altitude drawn to the hypotenuse. How do I find the value of x, y and z?

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1 Answer
Jim G.
Nov 22, 2017

#"see explanation"#

Explanation:

#color(blue)"diagram on left"#

#"within the diagram there are 3 right triangles"#

#"using "color(blue)"Pythagoras' theorem"#

#color(blue)"small triangle on left"#

#y^2=x^2+4to(1)#

#color(blue)"larger triangle on right"#

#z^2=x^2+64to(2)#

#color(blue)"outer main triangle"#

#y^2+z^2=100to(3)#

#"substitute equation "(1)" into equation "(3)#

#x^2+4+z^2=100#

#"substitute equation "(2)" into this equation"#

#x^2+4+x^2+64=100larrcolor(red)"equation in one variable"#

#rArr2x^2=32rArrx^2=16rArrx=4#

#"substitute this value into equation "(1)#

#y^2=16+4rArry^2=20rArry=2sqrt5#

#"substitute x = 4 into equation "(2)#

#z^2=16+64rArrz^2=80rArrz=4sqrt5#

#"the diagram on the right is done in a similar way"#

#"you may wish to attempt it yourself for the practice"#

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