Question

The hypotenuse of a right triangle is 3 cm and one of the legs is 1 cm. What is the length of the other leg? Give an exact answer (that means do not use your calculator to get a decimal).

Answer 1

The length of the other leg is
`2√(2)` cm.

Explanation:

In a right triangle, if the length of two legs are
`a` and
`b`, and the length of hypotenuse is
`c`, then according to the Pythagorean theorem:
`a^2+b^2= c^2`

Here, the hypotenuse is 3 cm and one of the legs is 1 cm. That means,
`c= 3` and
`a=1`

Using the Pythagorean theorem.....

`(1)^2+b^2= (3)^2\\ \\ 1+b^2=9\\ \\ b^2=9-1\\ \\ b^2=8\\ \\ b=√(8)=√(4*2)=2√(2)`

So, the length of the other leg is
`2√(2)` cm.

Answer 2

Using the Pythagorean theorem we can solve for the missing leg.

The equation is a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.

Filling in a and c with the information provided we will solve for b ( the missing leg).

1^2 + b^2 = 3^2

1 + b^2 = 9

b^2 = 9-1

b^2 = 8

b = SQRT(8)

b = 2 SQRT(2)