ABC is a triangle right angled at B. Further, (AB + BC) exceeds AC by 10 units. If the perimeter of the triangle is 60 units, then what is the area of the triangle?

Explanation

Given AB + BC + AC = 60 and AB + BC = AC + 10. Substituting the second into the first: 2AC + 10 = 60 \Rightarrow AC = 25. So, AB + BC = 35. Using Pythagoras, AB^2 + BC^2 = 25^2 = 625. Solving AB + BC = 35 and AB^2 + BC^2 = 625 gives sides 15 and 20. Area = \frac{1}{2} \times 15 \times 20 = 150 square units.

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