Question

The three sides of a triangle are 7 cm, 9 cm and 8 cm. What is the area of the triangle?

• A. 12√3 Sq. cm
• B. 10√3 Sq. cm
• C. 12√5 Sq. cm
• D. 2√5 Sq. cm

Answer 1

Answer:

C. 12√5 Sq. cm

Solution: Given: Length of the three sides of the triangle: 7 cm, 9 cm, and 8 cm Formula used: To find the area of a triangle when the lengths of all three sides are known, we can use Heron's formula: Area = √(s(s - a)(s - b)(s - c)) Where: s = (a + b + c)/2 (semi-perimeter of the triangle) a, b, c = lengths of the three sides Calculation: Using the formula: s = (a + b + c)/2 s = (7 + 9 + 8)/2 s = 24/2 s = 12 cm Now, plug the values of a, b, c, and s into Heron's formula to find the area of the triangle: √(s(s - a)(s - b)(s - c)) √(12(12 - 7)(12 - 9)(12 - 8)) √(12 × 5 × 3 × 4) 12√5 Sq. cm Therefore, the area of the triangle with side lengths 7 cm, 9 cm, and 8 cm is approximately 12√5 Sq. cm