1Cademy - Finding the Dimensions of a Right-Triangular Boats Sail

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The Pythagorean Theorem

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Finding the Dimensions of a Right-Triangular Boat's Sail

Apply the Pythagorean Theorem and the seven-step problem-solving strategy to find the unknown leg lengths of a right triangle when the hypotenuse and the relationship between the legs are known.

Problem: A boat’s sail is in the shape of a right triangle. The hypotenuse is $17$ feet long. One side is $7$ feet less than the other side. Find the lengths of the sides of the sail.

Read: Determine that the problem involves a right-triangular sail where the hypotenuse is $17$ feet and one leg is $7$ feet shorter than the other.
Identify: The lengths of the two sides (legs) of the sail.
Name: Let $x$ = the length of one side. The other side is $x - 7$ .
Translate: Write the Pythagorean Theorem formula ( $a^2 + b^2 = c^2$ ) and substitute the expressions: $x^2 + (x - 7)^2 = 17^2$
Solve: Expand and simplify: $x^2 + x^2 - 14x + 49 = 289$ $2x^2 - 14x + 49 = 289$ Bring all terms to one side to set the quadratic equation to zero: $2x^2 - 14x - 240 = 0$ Factor out the greatest common factor ( $2$ ): $2(x^2 - 7x - 120) = 0$ Factor the trinomial: $2(x - 15)(x + 8) = 0$ Use the Zero Product Property: $x - 15 = 0 \quad ext{or} \quad x + 8 = 0$ $x = 15 \quad ext{or} \quad x = -8$ Discard the negative solution since a physical side length cannot be negative. Thus, $x = 15$ . The length of the other side is $15 - 7 = 8$ .
Check: Verify using the Pythagorean Theorem: $8^2 + 15^2 = 64 + 225 = 289$ and $17^2 = 289$ . $289 = 289$ $\checkmark$
Answer: The sides of the sail are $8$ feet, $15$ feet, and $17$ feet.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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