What is the area of the triangle ABC?
Consider the following for the next two (02) items that follow :<br>ABC is a triangle right-angled at B. The perimeter of the triangle is 24 cm and the difference between the sum of the perpendicular sides and the hypotenuse is 4 cm.
- A. 18 square cm
- B. 24 square cm ✓
- C. 36 square cm
- D. 48 square cm
Correct Answer: B. 24 square cm
Explanation
Let perpendicular sides be a, c and hypotenuse be b. Perimeter a+b+c=24 and (a+c)-b=4. Adding them gives 2(a+c)=28 \implies a+c=14. Then b=10. We know a^2+c^2 = b^2 = 100. From (a+c)^2 = 196, we get 100 + 2ac = 196 \implies ac = 48. Area = \frac{1}{2}ac = 24 sq cm.
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