Determine the required dimensions for the construction project.

Cevap:A construction crew is building a wooden ramp with a right triangular cross-section. The horizontal base of the ramp measures

24\text{ feet}

and it rises to a vertical height of

7\text{ feet}

. According to the Pythagorean Theorem, the length of the sloped surface is 【25】 feet, and the total perimeter of the ramp's triangular profile is 【56】 feet.

Cevap

The sloped surface is 25 feet, and the total perimeter is 56 feet.

The sloped surface corresponds to the hypotenuse of a right triangle with legs of

7

and

24

feet. Applying the Pythagorean Theorem,

7^2 + 24^2 = 49 + 576 = 625

. Taking the square root of

625

gives

25\text{ feet}

for the sloped surface. The total perimeter is the sum of the base, height, and sloped surface:

24 + 7 + 25 = 56\text{ feet}

Adım Adım Çözüm

Identify the known sides of the right triangle.

The legs of the right triangle are

a = 7

and

b = 24

The horizontal base and vertical height form the two legs that intersect at a right angle.

Apply the Pythagorean Theorem to find the length of the hypotenuse.

c^2 = 7^2 + 24^2 = 49 + 576 = 625

. Therefore,

c = \sqrt{625} = 25

The sloped surface represents the hypotenuse (

c

) of the right triangle.

Calculate the perimeter of the triangle.

7 + 24 + 25 = 56

The perimeter is found by summing the lengths of all three sides of the triangular cross-section.

Anahtar Kavram

Using the Pythagorean Theorem to find the hypotenuse of a right triangle, and applying it to calculate the perimeter.

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