Two legs of a right triangle are two consecutive even integers. The hypotenuse is 10 inches. Use the quadratic formula in the process to find the measure of both missing legs?

1 Answer
Shiva Prakash M V
Mar 2, 2018

Missing legs are 6 and 8

Explanation:

Let x-1 be one of the leg
x-1 is an even number
the consecutive even number is x-1+2=x+1
hypotenuse is 10
Sum of squares of the legs
#(x-1)^2+(x+1)^2#
Square of hypotenuse
#10^2#
Using pythagoras theorem
#(x-1)^2+(x+1)^2=10^2#
#(x-1)^2+(x+1)^2=2(x^2+1)#
#2(x^2+1)=100#
#x^2+1=100/2#
#x^2+1=50#
#x^2=50-1#
#x^2=49#
Taking square roots
#x=sqrt49#
#x=7#
One of the leg is
#x-1=7-1=6#
The other leg is
#x+1=7+1=8#

Missing legs are 6 and 8

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