How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: side 1: x + 7, side 2: 35, side 3: x?

1 Answer
Shwetank Mauria
Jul 31, 2016

Solutions are #91#, #35# and #84#

or #21#, #28# and #35#.

Explanation:

Pythagoras theorem states that in a right angled triangle, square of the hypotenuse the largest side is equal to sum of squares of other two sides.

As the larges side is hypotenuse, either side 1 or side 2 could be hypotenuse. Note side 3 cannot be hypotenuse as side 1 is greater than side 3. Hence, there could be two possibilities.

1 - If #x+7# is hypotenuse than

#(x+7)^2=35^2+x^2# or #x^2+14x+49=35^2+x^2# or

#14x=35^2-49=1225-49=1176# or #x=1176/14=84# and sides are

#91#, #35# and #84#

2 - If #35# is hypotenuse than

#(x+7)^2+x^2=35^2# or #x^2+14x+49+x^2=1225# or

#2x^2+14x-1176=0# or #x^2+7x-588=0# and

#x=(-7+-sqrt(7^2-4xx1xx(-588)))/2=(-7+-sqrt(49+2352))/2#

or #x=(-7+-sqrt2401)/2=(-7+-49)/2#

But as using minus sign gives negative answer, which is not possible, only possibility is #x=(-7+49)/2=42/2=21# and sides are #21#, #28# and #35#.

Hence solutions are #91#, #35# and #84#

or #21#, #28# and #35#.

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