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. What is the area of the triangle ABC?
A.18 square cm
B.24 square cm✓ Correct
C.36 square cm
D.48 square cm
Explanation
Let perpendicular sides be a, b and hypotenuse c. a + b + c = 24, (a + b) - c = 4. Adding: 2(a+b) = 28, a + b = 14. Then c = 10. So a² + b² = 100 and a + b = 14. (a+b)² = 196 = a² + b² + 2ab = 100 + 2ab, so 2ab = 96, ab = 48. Area = ab/2 = 24 sq cm.
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