UPSC CDS I 2025 Mathematics Paper

Given:
‌p+b+h=24
‌p+b−h=4
Formula used:
The radius ( r ) of the inscribed circle in a right-angled triangle is given by the formula:
r=‌

p+b−h

2

Where: p and b are the perpendicular sides of the triangle
Area of triangle = radius (r) of the inscribed circle × semi - perimeter .
c is the hypotenuse of the triangle
Calculation:
‌p+b+h=24cm
‌p+b−h=4cm
The radius ( r ) of the inscribed circle in a right-angled triangle is given by the formula:
‌r=‌

p+b−h

2

‌r=4∕2=2cm
Area of triangle =2×24∕2=24cm2