Question

if the hypotenuse of a right triangle is 10 units and one leg is 6 units, what is the length of the other leg?
a. 5 units
b. 7 units
c. 4 units
d. 8 units

in a right triangle, if the legs are equal in length, and each is √2, what is the hypotenuse?
a. √5
b. √3
c. 2
d. 1

Explanation:

Step1: Apply Pythagorean theorem for first - question

Let the hypotenuse be $c$, one leg be $a$ and the other leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Given $c = 10$ and $a = 6$, we can find $b$ as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Calculate the value of $b$

$b=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$

Step3: Apply Pythagorean theorem for second - question

Let the two legs be $a = b=\sqrt{2}$, and the hypotenuse be $c$. By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$.

Step4: Calculate the value of $c$

$c=\sqrt{(\sqrt{2})^{2}+(\sqrt{2})^{2}}=\sqrt{2 + 2}=\sqrt{4}=2$

Answer:

1. d. 8 units
2. c. 2