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
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.