The hypotenuse of a right angled triangle is of length square root34. The sum of the other two sides is 8. How do you find the length of each side?

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The hypotenuse of a right angled triangle is of length square root34. The sum of the other two sides is 8. How do you find the length of each side?

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Answer 1 · 2016-02-12T23:57:17

I found $3 and 5$ $3 and 5$

Explanation:

We can use Pythagoras theorem where $a$ $a$ and $b$ $b$ are the two sides and $c = \sqrt{34}$ $c=sqrt(34)$ is the hipotenuse to get:
$c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$
you also know that $a + b = 8$ $a+b=8$
or $a = 8 - b$ $a=8-b$ into $c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$ you get:
$34 = {(8 - b)}^{2} + b^{2}$ $34=(8-b)^2+b^2$
$34 = 64 - 16 b + b^{2} + b^{2}$ $34=64-16b+b^2+b^2$
$2 b^{2} - 16 b + 30 = 0$ $2b^2-16b+30=0$
Using the Quadratic Formula:
$b_{1, 2} = \frac{16 \pm \sqrt{256 - 240}}{4} = \frac{16 \pm 4}{4}$ $b_(1,2)=(16+-sqrt(256-240))/4=(16+-4)/4$
getting:
$b_{1} = 5$ $b_1=5$
$b_{2} = 3$ $b_2=3$
and:
$a_{1} = 8 - 5 = 3$ $a_1=8-5=3$
$a_{2} = 8 - 3 = 5$ $a_2=8-3=5$

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The hypotenuse of a right angled triangle is of length square root34. The sum of the other two sides is 8. How do you find the length of each side?

1 Answer

Explanation:

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