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Zorluk: OrtaTriangles and Pythagorean Theorem

Provide the missing numerical values to complete the calculations for the stage construction.

Cevap:A theater crew is reinforcing a rectangular stage that measures 1616 feet in width and 3030 feet in length. They place a diagonal steel support beam underneath, running directly from one corner to the opposite corner. By applying the Pythagorean theorem, the length of this diagonal support beam is calculated to be 【34】 feet. Consequently, the total perimeter of the right triangle formed by the width, length, and the new diagonal beam is 【80】 feet.

Cevap

The diagonal support beam is 34 feet long, and the total perimeter of the right triangle is 80 feet.
The width and length of the rectangular stage act as the two legs of a right triangle. Using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we substitute the known legs: 162+302=256+900=115616^2 + 30^2 = 256 + 900 = 1156. The square root of 11561156 is 3434, so the diagonal hypotenuse is 3434 feet. The perimeter of this triangle is the sum of its three sides: 16+30+34=8016 + 30 + 34 = 80 feet.

Adım Adım Çözüm

1
Identify the lengths of the two legs of the right triangle formed by the stage's dimensions.
Leg a = 16 feet, Leg b = 30 feet.
The width and length of a rectangle meet at a 90-degree angle, serving as the legs of the right triangle.
2
Apply the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to calculate the hypotenuse.
162+302=256+900=115616^2 + 30^2 = 256 + 900 = 1156. Taking the square root, c=1156=34c = \sqrt{1156} = 34 feet.
The diagonal beam forms the hypotenuse of the right triangle spanning opposite corners.
3
Calculate the perimeter of the newly formed right triangle.
Perimeter = 16+30+34=8016 + 30 + 34 = 80 feet.
The perimeter of a triangle is the total sum of its three side lengths.

Anahtar Kavram

Applying the Pythagorean theorem to find a missing hypotenuse, and calculating the perimeter of a right triangle.
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Konular

Triangles and Pythagorean Theorem

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