The length of the hypotenuse of a right triangle is 13 m. The length of one leg is 5 cm. Find the length of the other leg.
a) 14 cm
b) 144 cm
c) 8 cm
d) 12 cm
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
Solve for b.
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, let's assume the length of the other leg is x cm. According to the Pythagorean theorem:
(5 cm)^2 + (x cm)^2 = (13 cm)^2
25 cm^2 + x^2 = 169 cm^2
To solve this equation, we subtract 25 cm^2 from both sides:
x^2 = 169 cm^2 - 25 cm^2
x^2 = 144 cm^2
To find the length of x, we take the square root of both sides:
x = √144 cm
x = 12 cm
Therefore, the length of the other leg of the right triangle is 12 cm. Hence, the correct option is d) 12 cm.