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An isosceles right triangle has a hypotenuse of length 4 inches. What (May 2023 U.S.)
An isosceles right triangle has a hypotenuse of length 4 inches.
What is the perimeter, in inches, of this triangle?
A. 2√2
B. 4√2
C. 4 + 4√2
D. 4 + 8√2
Solution
Correct answer: C. 4 + 4√2.
Since it's an isosceles right triangle, the two legs are equal in length. Let's call the length of each leg x.
Using the Pythagorean theorem, we can set up the equation:
x² + x² = 4²
Combine like terms:
2x² = 16
Divide both sides by 2:
x² = 8
Take the square root of both sides:
x = √8
Since it's an isosceles right triangle, the length of each leg is √8.
The perimeter is the sum of the lengths of all three sides:
Perimeter = x + x + 4 = 2√8 + 4
Simplify:
Perimeter = 2√8 + 4
Exam Edition: May 2023 U.S.
Exam Year: 2023
Related topics: Geometry, Trigonometry