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Find the area of a triangle with two sides measuring 16 cm and 22 cm, and a perimeter of 64 cm.

A) 175.2 cm\(^2\)
B) 176 cm\(^2\)
C) 184 cm\(^2\)
D) 192 cm\(^2\)

Answer :

Final answer:

The area of the triangle is calculated by using Heron's formula, given the lengths of the sides and the perimeter. The area approximates to 176 cm^2. The correct answer is option b).

Explanation:

To find the area of the triangle, we must first identify the length of the third side. We know that the perimeter of a triangle is the sum of its sides, in this case 64 cm. So, the length of the third side is 64 cm - 16 cm - 22 cm, which equals 26 cm.

Next, we use the formula for the area of a triangle using Heron's formula, which is suitable for when we have the length of all sides. Heron's formula is √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.

Semi-perimeter, s = (a + b + c )/2 = (16 cm + 22 cm + 26 cm) / 2 = 32 cm.

We substitute the values into Heron's formula: area = √32(32 - 16)(32 - 22)(32 - 26)

The result gives us the area of the triangle, which is approximately 176 cm^2. Therefore, the correct choice is b).

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