To find the longest altitude of a triangle, we first need to identify the longest side of the triangle. In this case, the longest side is 15 cm. This will be the base of the triangle when calculating the longest altitude.

The formula for the area of a triangle is 1/2 * base * height. We can rearrange this formula to solve for the height (which is the same as the altitude in this case): height = (2 * area) / base.

However, we don't know the area of the triangle yet. We can find this using Heron's formula, which is suitable for any type of triangle: area = sqrt[s(s - a)(s - b)(s - c)], where a, b, and c are the sides of the triangle and s is the semi-perimeter of the triangle.

First, let's find s: s = (a + b + c) / 2 = (13 + 14 + 15) / 2 = 21 cm.

Now we can find the area: area = sqrt[21(21 - 13)(21 - 14)(21 - 15)] = sqrt[21*8*7*6] = 84 cm^2.

Finally, we can find the longest altitude: height = (2 * 84) / 15 = 11.2 cm. So, the longest altitude of the triangle is 11.2 cm.

Question

To find the longest altitude of a triangle, we first need to identify the longest side of the triangle. In this case, the longest side is 15 cm. This will be the base of the triangle when calculating the longest altitude.

The formula for the area of a triangle is 1/2 * base * height. We can rearrange this formula to solve for the height (which is the same as the altitude in this case): height = (2 * area) / base.

However, we don't know the area of the triangle yet. We can find this using Heron's formula, which is suitable for any type of triangle: area = sqrt[s(s - a)(s - b)(s - c)], where a, b, and c are the sides of the triangle and s is the semi-perimeter of the triangle.

First, let's find s: s = (a + b + c) / 2 = (13 + 14 + 15) / 2 = 21 cm.

Now we can find the area: area = sqrt[21(21 - 13)(21 - 14)(21 - 15)] = sqrt[21*8*7*6] = 84 cm^2.

Finally, we can find the longest altitude: height = (2 * 84) / 15 = 11.2 cm. So, the longest altitude of the triangle is 11.2 cm.

Knowee AI · Accepted Answer

To find the longest altitude of a triangle, we first need to identify the longest side of the triangle. In this case, the longest side is 15 cm. This will be the base of the triangle when calculating the longest altitude.

The formula for the area of a triangle is 1/2 * base * height. We can rearrange this formula to solve for the height (which is the same as the altitude in this case): height = (2 * area) / base.

However, we don't know the area of the triangle yet. We can find this using Heron's formula, which is suitable for any type of triangle: area = sqrt[s(s - a)(s - b)(s - c)], where a, b, and c are the sides of the triangle and s is the semi-perimeter of the triangle.

First, let's find s: s = (a + b + c) / 2 = (13 + 14 + 15) / 2 = 21 cm.

Now we can find the area: area = sqrt[21(21 - 13)(21 - 14)(21 - 15)] = sqrt[21*8*7*6] = 84 cm^2.

Finally, we can find the longest altitude: height = (2 * 84) / 15 = 11.2 cm. So, the longest altitude of the triangle is 11.2 cm.

A triangle with sides 13 cm, 14 cm and 15 cmLongest altitude (La) in cm

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