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Mekhanik
2 months ago
12

The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24. Find the area of the triangle

Mathematics
1 answer:
lawyer [12.5K]2 months ago
5 0

When the sides are in a ratio of 11:16:24, it suggests they are multiples of a common variable x, based on these proportions.

The shortest side measures 11x feet, the middle side is 16x feet, and the longest measures 24x feet.

This indicates a perimeter of

11x+16x+24x = 51x feet. Given that the actual perimeter is 510 feet, we have:

51x = 510 \implies x = \cfrac{510}{51} = 10.

Thus, the sides measure 110, 160, and 240 feet each.

To determine the area of the triangle with these three sides, Heron's formula is applicable. This formula states that, if s represents half of the perimeter for a triangle with sides a,b,c, the area A is given by:

A = \sqrt{s(s-a)(s-b)(s-c)}

In this scenario, s = 255, a = 110, b = 160, c = 240, so the formula adapts to:

A = \sqrt{255(255-110)(255-160)(255-240)} = \sqrt{255(145)(95)(15)} = \sqrt{52689375} \approx 7258.74

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Answer:

Step-by-step explanation:

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a) P(X\leq 15) = 0.1565=0.157

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2 months ago
A gazebo is being built near a nature trail. An equation of the line representing the nature trail is y = 13x−4. Each unit in th
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Respuesta:

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Explicación paso a paso:

Dado que:

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This may be a bit awkward to explain in writing, so please bear with me:)

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