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

ANSWER:

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,  

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

$\mathrm{H}^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}$

$11^{2}=3^{2}+b^{2}$      

$121=9+b^{2}$  

$b^{2}=121-9$    

$\mathrm{b}^{2}=112$

$\mathrm{b}=\sqrt[2]{112}$  

$\mathrm{b}=\sqrt[2]{16 \times 7}$

$\mathrm{b}=\sqrt[2]{16} \times \sqrt[2]{7}$

$b=4 \sqrt[2]{7}$    

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