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Zorluk: OrtaTriangles and Pythagorean Theorem

A right-angled triangular warning sign is being designed for a factory floor. The longest side of the sign measures 17 inches17\text{ inches}, and one of its perpendicular sides measures 8 inches8\text{ inches}. What is the total area of the front face of the sign?

  1. A
    36 square inches36\text{ square inches}
  2. B
    40 square inches40\text{ square inches}
  3. 60 square inches60\text{ square inches}Cevap
  4. D
    68 square inches68\text{ square inches}

Cevap

60 square inches60\text{ square inches}
To find the area of a right triangle, the lengths of both perpendicular legs must be known. Using the Pythagorean theorem, the missing leg is calculated as 15 inches15\text{ inches} (since 172−82=15\sqrt{17^2 - 8^2} = 15). The area is then found by multiplying one half by the product of the two legs (0.5×8×15=600.5 \times 8 \times 15 = 60).

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1
Identify the given sides of the right triangle.
The hypotenuse (longest side, cc) is 17 inches17\text{ inches} and one leg (aa) is 8 inches8\text{ inches}.
The area formula for a right triangle requires the lengths of both perpendicular legs, not the hypotenuse.
2
Use the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to find the missing leg (bb).
82+b2=1728^2 + b^2 = 17^2, which simplifies to 64+b2=28964 + b^2 = 289. Solving for b2b^2 gives 225225, so b=15 inchesb = 15\text{ inches}.
Both perpendicular legs are needed to establish the base and height of the triangle.
3
Calculate the area of the triangle using the formula Area = 0.5×base×height0.5 \times \text{base} \times \text{height}.
Area = 0.5×8×15=60 square inches0.5 \times 8 \times 15 = 60\text{ square inches}.
The two legs of a right triangle serve as its base and height.

Anahtar Kavram

Pythagorean Theorem and Triangle Area
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Konular

Triangles and Pythagorean Theorem

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