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Kenneth wants to sew a tent, including the bottom so that it is entirely enclosed. He has a rectangular piece of canvas with dimensions of 12 feet by 20 feet. The front and back of the tent will be identical triangles, measuring 6 feet across at ground level, with two 5-foot sides meeting at the top. The depth of the tent will be equal to three times the height of the front of the tent. What is the depth of the tent?

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Lanuel

Based on the calculations, the depth of tent is equal to 12 feet.

How to calculate the depth of the tent?

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

  • Triangle ABC is an isosceles triangle (AB = AC).
  • The front and back of the triangle are identical triangles.
  • Side AD is perpendicular side BC.
  • CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

AD² = AC² - DC²

AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

Where:

  • b is the base area.
  • h is the height.

Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

Read more on area of triangle here: brainly.com/question/21917592

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Ver imagen Lanuel

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