In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?
Practice Questions
1 question
Q1
In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?
84 cm²
96 cm²
120 cm²
140 cm²
Using Heron's formula, the semi-perimeter s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84 cm².
Questions & Step-by-step Solutions
1 item
Q
Q: In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?
Solution: Using Heron's formula, the semi-perimeter s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84 cm².
Steps: 9
Step 1: Identify the lengths of the sides of triangle ABC. We have AB = 7 cm, AC = 24 cm, and BC = 25 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (AB + AC + BC) / 2.
Step 3: Substitute the values into the formula: s = (7 + 24 + 25) / 2 = 28 cm.
Step 4: Use Heron's formula to find the area of the triangle. The formula is Area = √[s(s-a)(s-b)(s-c)], where a, b, and c are the lengths of the sides.
Step 5: Substitute the values into Heron's formula: Area = √[28(28-7)(28-24)(28-25)].
