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Zorluk: OrtaTriangles and Pythagorean Theorem

A stained glass artist cuts a piece of glass into the shape of a right triangle. The two perpendicular legs of the triangle measure 3030 centimeters and 4040 centimeters. What is the total perimeter of this glass triangle in centimeters?

Cevap: 120 cm

Cevap

120
The correct answer is found by first determining the length of the hypotenuse using the Pythagorean theorem. Since the legs are 3030 and 4040, the hypotenuse is 302+402=2500=50\sqrt{30^2 + 40^2} = \sqrt{2500} = 50. The perimeter is then calculated by adding the lengths of all three sides: 30+40+50=12030 + 40 + 50 = 120.

Adım Adım Çözüm

1
Use the Pythagorean theorem to find the length of the missing hypotenuse.
c=302+402=900+1600=2500=50c = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50 centimeters.
The perimeter requires all three side lengths, but only the two legs are provided.
2
Calculate the total perimeter of the right triangle.
Perimeter = 30+40+50=12030 + 40 + 50 = 120 centimeters.
The perimeter is the total distance around the outside of the shape, found by summing all side lengths.

Anahtar Kavram

Applying the Pythagorean theorem to find a missing side length, then using all three side lengths to calculate the perimeter of a right triangle.
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Konular

Triangles and Pythagorean Theorem

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