A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of 196 centimeters (cm), and the tent is 250cm long. What is the height, in centimeters, of the tent? Choose 1 answer: (A) 98 (B) 98sqrt3 (c) 125sqrt3 (D) 196sqrt3

Problem Understanding: Understand the problem. We need to find the height of the equilateral triangular face of the tent. The sides of the triangular face are all 196 cm.Equilateral Triangle Properties: Recall the properties of an equilateral triangle. In an equilateral triangle, all sides are equal, and the height can be found using the formula for the height (h) of an equilateral triangle with side length (a): h = (sqrt(3)/2) * a.Applying the Formula: Apply the formula to find the height. Since each side of the triangle is 196 cm, we use the formula h = (sqrt(3)/2) * 196.Calculating the Height: Calculate the height. h = (sqrt(3)/2) * 196 = 98sqrt(3) cm.Verifying the Answer Choices: Verify the answer choices. The height calculated matches answer choice (B) 98sqrt3.

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A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of $196$ centimeters $(\mathrm{cm})$ , and the tent is $250 \mathrm{~cm}$ long. What is the height, in centimeters, of the tent? $\newline$ Choose $1$ answer: $\newline$ (A) $98$ $\newline$ (B) $98 \sqrt{3}$ $\newline$ (C) $125 \sqrt{3}$ $\newline$ (D) $196 \sqrt{3}$

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Algebra 2

Pythagorean Theorem and its converse

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Q. A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of

196

centimeters

(\mathrm{cm})

, and the tent is

250 \mathrm{~cm}

long. What is the height, in centimeters, of the tent?

\newline

Choose

1

answer:

\newline

(A)

98

\newline

(B)

98 \sqrt{3}

\newline

(C)

125 \sqrt{3}

\newline

(D)

196 \sqrt{3}

Problem Understanding: Understand the problem. $\newline$ We need to find the height of the equilateral triangular face of the tent. The sides of the triangular face are all $196\,\text{cm}$ .
Equilateral Triangle Properties: Recall the properties of an equilateral triangle. $\newline$ In an equilateral triangle, all sides are equal, and the height can be found using the formula for the height $h$ of an equilateral triangle with side length $a$ : $h = (\sqrt{3}/2) \cdot a$ .
Applying the Formula: Apply the formula to find the height. $\newline$ Since each side of the triangle is $196\,\text{cm}$ , we use the formula $h = \left(\frac{\sqrt{3}}{2}\right) \times 196$ .
Calculating the Height: Calculate the height. $h = (\frac{\sqrt{3}}{2}) \times 196 = 98\sqrt{3}$ cm.
Verifying the Answer Choices: Verify the answer choices. $\newline$ The height calculated matches answer choice (B) $98\sqrt{3}$ .