Question

the leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle? (4 points)

Answer 1

Length of the third side of right triangle is
`4 \sqrt[2]{7} \text { units }`

SOLUTION:

Given, two sides of a right triangle is 3 units and 11 units.

We need to find the length of third side.

Let, length of first side be “a” i.e. a = 3

Length of hypotenuse be “h” i.e. h = 11

Length of second side be “b” and b =?

We know that, for a right angle triangle,

`(\text { Hypotenuse })^(2)=(\text { side } 1)^(2)+(\text { side } 2)^(2)`

`\mathrm{H}^(2)=\mathrm{a}^(2)+\mathrm{b}^(2)`

`11^(2)=3^(2)+b^(2)`

`121=9+b^(2)`

`b^(2)=121-9`

`\mathrm{b}^(2)=112`

`\mathrm{b}=\sqrt[2]{112}`

`\mathrm{b}=\sqrt[2]{16 * 7}`

`\mathrm{b}=\sqrt[2]{16} * \sqrt[2]{7}`

`b=4 \sqrt[2]{7}`

hence, length of the third side of right triangle is
`4 \sqrt[2]{7} \text { units }`