The length of three altitude of a triangle are 6h,4h and 3h unit and…

TurquoiseBoar43

-6

Let the sides of the triangle be a, b, and c. Then, we have: a + b + c = 18 Also, we know that: a = 2h + 3h = 5h b = 2h + 4h = 6h c = 3h Substituting these values in the equation for the perimeter, we get: 5h + 6h + 3h = 18 Simplifying, we get: 14h = 18 Therefore, h = 9/7 Substituting this value of h in the expressions for a, b, and c, we get: a = 45/7 b = 54/7 c = 27/7 Therefore, the sides of the triangle are 45/7, 54/7, and 27/7 units long. To find the area of the triangle, we can use Heron's formula: s = (a + b + c)/2 = 18/2 = 9 Area = sqrt(s(s-a)(s-b)(s-c)) Substituting the values of s, a, b, and c, we get: Area = 54/7 sq. units

May 25, 2023

Sebrin

7

Let the sides of the triangle be a, b, and c. Then we have: a = 2/3 * 6h = 4h b = 2/3 * 4h = 8/3 * h c = 2/3 * 3h = 2h The perimeter of the triangle is given by: a + b + c = 4h + 8/3 * h + 2h = 18 Simplifying this equation, we get: 14h/3 = 18 Solving for h, we get: h = 27/14 Substituting this value of h back into the expressions for a, b, and c, we get: a = 4h = 54/7 b = 8/3 * h = 72/14 c = 2h = 54/14 To find the area of the triangle, we can use Heron's formula: s = (a + b + c)/2 = (54/7 + 72/14 + 54/14)/2 = 27/7 A = sqrt(s(s-a)(s-b)(s-c)) = sqrt(27/7 * (27/7 - 54/7) * (27/7 - 72/14) * (27/7 - 54/14)) = sqrt(972/343) = 6sqrt(12)/7 Therefore, the lengths of the sides of the triangle are a = 54/7, b = 72/14, and c = 54/14, and the area of the triangle is 6sqrt(12)/7.

May 25, 2023

Ano_nym_ous

1064

chatgpt?

May 25, 2023

27f

10

To solve this problem, first, let's denote the lengths of the sides of the triangle as a, b, and c. We are given that the altitudes of the triangle are 6h, 4h, and 3h units, and the perimeter is 18 units. Therefore, we have: a + b + c = 18 We also know the formula for the area of a triangle, which can be written in terms of its sides and altitudes as follows: Area = 0.5 * a * altitude_a = 0.5 * b * altitude_b = 0.5 * c * altitude_c Let's denote the area of the triangle as A. We can then write the following equations using the given altitudes: A = 0.5 * a * 6h A = 0.5 * b * 4h A = 0.5 * c * 3h Now, let's solve these equations for a, b, and c in terms of A and h: a = A / (3h) b = A / (2h) c = A / (1.5h) Now let's substitute these expressions for a, b, and c into the perimeter equation: A / (3h) + A / (2h) + A / (1.5h) = 18 To solve this equation for A/h, first, let x = A/h: x/3 + x/2 + x/1.5 = 18 Combining the terms, we have: (1/3 + 1/2 + 1/1.5) x = 18 (1/6) x = 18 Now, we can solve for x: x = 18 * 6 x = 108 Now we found that A/h = 108. We can use this to find the lengths of the sides: a = 108 / (3h) = 36/h b = 108 / (2h) = 54/h c = 108 / (1.5h) = 72/h Now, find the area A of the triangle: A = 0.5 * a * 6h = 0.5 * (36/h) * 6h = 0.5 * 36 * 6 = 108 square units Now, we have everything we need: Lengths of the sides: Side a = 36/h Side b = 54/h Side c = 72/h Area of the triangle: A = 108 square units Since we do not have any information about h, we can only express the sides in terms of h. The area of the triangle is 108 square units. Join CryptoAI | Chart | Buy

May 26, 2023

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