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The perimeter of the isosceles right angled triangle whose one leg is of 3 ft is given by: Option C: 6 + 3√2 ft
What is an isosceles right angled triangle?
It has two equal sides, and those two equal sides make 90 degrees (right angle) internally.
Referring to the figure, assuming:
- Both equal sides are of length 'a' feet
- The unequal side is of the length 'b' feet.
Using the Pythagoras theorem, we get:
[tex]a^2 + a^2 = b^2\\\\a = b/\sqrt{2}[/tex]
It was given that length of one of the leg is of 3 ft. Leg of an isosceles triangle refers to one of its equal sides.
Thus, we got [tex]a = 3[/tex], and therefore, we have: [tex]a = b/\sqrt{2} \implies b = a\sqrt{2} = 3\sqrt{2}[/tex]
Thus, perimeter of the triangle as:
[tex]a + a + b = 2a + b = 6 +3\sqrt{2} \: \rm ft[/tex]
Thus, the perimeter of the isosceles right angled triangle whose one leg is of 3 ft is given by: Option C: 6 + 3√2 ft
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
Answer:
C : 6 + 3√2 ft
Step-by-step explanation:
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