ANSWER:
Length of the third side of right triangle is [tex]4 \sqrt[2]{7} \text { units }[/tex]
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,
[tex](\text { Hypotenuse })^{2}=(\text { side } 1)^{2}+(\text { side } 2)^{2}[/tex]
[tex]\mathrm{H}^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}[/tex]
[tex]11^{2}=3^{2}+b^{2}[/tex]
[tex]121=9+b^{2}[/tex]
[tex]b^{2}=121-9[/tex]
[tex]\mathrm{b}^{2}=112[/tex]
[tex]\mathrm{b}=\sqrt[2]{112}[/tex]
[tex]\mathrm{b}=\sqrt[2]{16 \times 7}[/tex]
[tex]\mathrm{b}=\sqrt[2]{16} \times \sqrt[2]{7}[/tex]
[tex]b=4 \sqrt[2]{7}[/tex]
hence, length of the third side of right triangle is [tex]4 \sqrt[2]{7} \text { units }[/tex]
