Question

If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Answer 1

Answer:

$5\sqrt{3}$ inches long is the other leg

Step-by-step explanation:

Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.

Hypotenuse side = 10 inches

Let length of other leg be x.

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

Then; by definition of Pythagoras theorem;

${\text}(Hypotenuse)^2 = (5)^2 + x^2$

$(10)^2 = 5^2 + x^2$

$100 = 25 + x^2$

Subtract 25 on both sides we get;

$100-25= 25 + x^2-25$

Simplify:

$75 = x^2$

Simplify:

$x = \sqrt{75} = 5\sqrt{3}$ inches

Therefore, the sides of other leg is $5\sqrt{3}$ inches