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?

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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?

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Answer 1 · 2016-07-31T17:59:59

Solutions are $91$ $91$ , $35$ $35$ and $84$ $84$

or $21$ $21$ , $28$ $28$ and $35$ $35$ .

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 $x + 7$ $x+7$ is hypotenuse than

${(x + 7)}^{2} = 35^{2} + x^{2}$ $(x+7)^2=35^2+x^2$ or $x^{2} + 14 x + 49 = 35^{2} + x^{2}$ $x^2+14x+49=35^2+x^2$ or

$14 x = 35^{2} - 49 = 1225 - 49 = 1176$ $14x=35^2-49=1225-49=1176$ or $x = \frac{1176}{14} = 84$ $x=1176/14=84$ and sides are

$91$ $91$ , $35$ $35$ and $84$ $84$

2 - If $35$ $35$ is hypotenuse than

${(x + 7)}^{2} + x^{2} = 35^{2}$ $(x+7)^2+x^2=35^2$ or $x^{2} + 14 x + 49 + x^{2} = 1225$ $x^2+14x+49+x^2=1225$ or

$2 x^{2} + 14 x - 1176 = 0$ $2x^2+14x-1176=0$ or $x^{2} + 7 x - 588 = 0$ $x^2+7x-588=0$ and

$x = \frac{- 7 \pm \sqrt{7^{2} - 4 \times 1 \times (- 588)}}{2} = \frac{- 7 \pm \sqrt{49 + 2352}}{2}$ $x=(-7+-sqrt(7^2-4xx1xx(-588)))/2=(-7+-sqrt(49+2352))/2$

or $x = \frac{- 7 \pm \sqrt{2401}}{2} = \frac{- 7 \pm 49}{2}$ $x=(-7+-sqrt2401)/2=(-7+-49)/2$

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

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

or $21$ $21$ , $28$ $28$ and $35$ $35$ .

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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

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