Question

A right triangle has legs that are 10 meters and 3 meters in length. How long is its hypotenuse?

Answer 1

We need to use the Phytagorean Theorem:

`\sf a^2+b^2=c^2`

Where 'a' and 'b' are the legs of the right triangle, and 'c' is the hyptotenuse.

So it wants to know the hypotenuse, so that means that '10' and '3' are the legs of the right triangle and we can substitute those numbers for 'a' and 'b' and solve for c.

So, plugging in the values for 'a' and 'b' :


`\sf 3^2+10^2=c^2`

We can now expand what
`\sf 3^2` and
`\sf 10^2` equal to:


`\sf 9+100 =c^2`

Now we add
`\sf 9` and
`\sf 100`


`\sf 109 = c^2`

So now we have to take the square root to get the value for 'c' or the hypotenuse:


`\sf c= √(109)`

And so the value of the hypotenuse will be
`\sf √(109)`

And if it wants the answer in decimal form, that would be:
`\sf 10.44`

Answer 2

Use the Pythagorean Theorem.

a^2 + b^2 = c^2

Where 'a' and 'b' are the two legs and 'c' is the hypotenuse.

Plug in what we know:

3^2 + 10^2 = c^2

Simplify the exponents:

9 + 100 = c^2

Add:

109 = c^2

Find the square root of both sides:

c = 10.44

So the Hypotenuse is approximately 10.44 meters long.