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Difficulty: EasyTriangles and Pythagorean Theorem

A sail on a small boat is shaped like a right triangle. The horizontal bottom edge of the sail is 77 feet long, and the vertical edge is 2424 feet high. What is the length, in feet, of the longest edge (the hypotenuse) of the sail?

Answer: 25 feet

Answer

25
The correct answer is found by applying the Pythagorean Theorem (a2+b2=c2a^2 + b^2 = c^2). Substituting the lengths of the two legs (77 and 2424), the equation becomes 72+242=c27^2 + 24^2 = c^2. Squaring the numbers yields 49+57649 + 576. Adding these together gives 625=c2625 = c^2. Finally, taking the square root of 625625 results in 2525, which represents the length of the hypotenuse.

Step-by-Step Solution

1
Identify the known sides of the right triangle.
Leg a=7a = 7 feet and leg b=24b = 24 feet.
The horizontal and vertical edges of the sail represent the two perpendicular legs of a right triangle.
2
Set up the Pythagorean Theorem equation.
72+242=c27^2 + 24^2 = c^2
The Pythagorean Theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse (cc).
3
Square the lengths of the legs.
49+576=c249 + 576 = c^2
To evaluate the equation, the individual lengths must be squared before adding them.
4
Add the squared values together.
625=c2625 = c^2
Combining the squared leg lengths yields the square of the hypotenuse.
5
Calculate the square root to solve for c.
c=25c = 25
Taking the square root of 625625 gives the final length of the hypotenuse.

Key Concept

Pythagorean Theorem
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Topics

Triangles and Pythagorean Theorem

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