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Zorluk: OrtaPerimeter and Area of 2D Figures

A canvas tarp is cut into the shape of a right triangle. The area of the tarp is 6060 square feet, and its shortest leg measures 88 feet. What is the perimeter of the tarp in feet?

  1. A
    2323
  2. 4040Cevap
  3. C
    4646
  4. D
    6060

Cevap

4040
To find the perimeter, all three sides of the right triangle are needed. Using the given area (6060) and shortest leg (88), the length of the other leg is found with the area formula A=12bhA = \frac{1}{2}bh, yielding 1515 feet. Next, the Pythagorean theorem (82+152=c28^2 + 15^2 = c^2) reveals the hypotenuse is 1717 feet. Summing the three sides (8+15+178 + 15 + 17) gives the correct perimeter of 4040 feet.

Adım Adım Çözüm

1
Find the length of the other leg using the area formula for a triangle, A=12bhA = \frac{1}{2}bh.
60=12(8)b⇒60=4b⇒b=1560 = \frac{1}{2}(8)b \Rightarrow 60 = 4b \Rightarrow b = 15 feet.
The perimeter requires all three side lengths, so the missing leg must be calculated first.
2
Use the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to find the hypotenuse.
82+152=c2⇒64+225=c2⇒289=c2⇒c=178^2 + 15^2 = c^2 \Rightarrow 64 + 225 = c^2 \Rightarrow 289 = c^2 \Rightarrow c = 17 feet.
The hypotenuse is the third side needed to find the complete outer boundary of the right triangle.
3
Calculate the perimeter by summing the three side lengths.
P=8+15+17=40P = 8 + 15 + 17 = 40 feet.
The perimeter of any polygon is the total length of its outer boundary.

Anahtar Kavram

Calculating missing dimensions of a right triangle using area and the Pythagorean theorem to find the perimeter.
Tahmini Süre:1m 0s
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Perimeter and Area of 2D Figures

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