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the radio of the sides of triangle is $2:6:7$ .if the perimeter of the triangle is $195$ meters what is the length of the longest side

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Find the length of the transverse or conjugate axes of a hyperbola

Full solution

Q. the radio of the sides of triangle is

2:6:7

.if the perimeter of the triangle is

195

meters what is the length of the longest side

Denote sides of triangle: Let's denote the sides of the triangle as $2x$ , $6x$ , and $7x$ , where $x$ is a common multiplier. The perimeter of the triangle is the sum of its sides. $\newline$ Perimeter = $2x + 6x + 7x$
Perimeter equation: Given that the perimeter is $195$ meters, we can set up the equation: $2x + 6x + 7x = 195$
Combine like terms: Combine like terms to simplify the equation: $15x = 195$
Solve for x: Divide both sides of the equation by $15$ to solve for x: $\newline$ $x = \frac{195}{15}$ $\newline$ $x = 13$
Find longest side length: Now that we have the value of $x$ , we can find the length of the longest side, which is $7x$ :
Longest side = $7 \times x$
Longest side = $7 \times 13$
Longest side = $91$ meters

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