Question

Find the area of a triangle whose perimeter is 180 cm, and its two sides are 80 cm and 18 cm. Calculate the altitude of the triangle corresponding to its shortest side.

a) 3600 cm², 36 cm
b) 3600 cm², 24 cm
c) 1800 cm², 36 cm
d) 1800 cm², 24 cm

Answer 1

To find the area of a triangle with a given perimeter and side lengths, we can first calculate the length of the third side. Then, we can use the formula for the area of a triangle to find the altitude corresponding to the shortest side.

Step-by-step explanation:

To find the area of a triangle, we can first calculate the length of the third side using the given perimeter and the lengths of the other two sides. Substituting the given values, we have: P = a + b + c => 180 = 80 + 18 + c => c = 82 cm. Next, we can use the equation for the area of a triangle, which is: A = 1/2 * base * height.

Since the altitude corresponding to the shortest side is the height of the triangle, we can use the formula A = 1/2 * b * h. Substituting the given values, we have: A = 1/2 * 18 * h => 82h = 3600 => h ≈ 43.9 cm.

Therefore, the altitude of the triangle corresponding to its shortest side is approximately 43.9 cm. The correct answer is option d) 1800 cm², 24 cm.