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MAT Exam 2025 Paper

Question : 76 of 150

Marks: +1, -0

\mathrm{Pq}=35 \mathrm{~cm}

\mathrm{PR}=12 \mathrm{~cm}

r

, the radius of the inscribed circle.

Solution:

Concept:

For a right-angled triangle, the radius

r

of the inscribed circle can be found using the two perpendicular sides and the hypotenuse.

Explanation:

\triangle \mathrm{PQR}

, the sides

\mathrm{PQ}=35

cm and

\mathrm{PR}=12

cm are the perpendicular sides.

So,

\mathrm{QR}

is the hypotenuse.

Using Pythagoras theorem:

\mathrm{QR}=\sqrt{\mathrm{PQ}^2+\mathrm{PR}^2}

=\sqrt{35^2+12^2}=\sqrt{1225+144}

=\sqrt{1369}=37

cm.

For a right triangle, the inradius is given by:

r=\frac{\text{Perpendicular side 1}+\text{Perpendicular side 2}-\text{Hypotenuse}}{2}

r=\frac{\mathrm{PQ}+\mathrm{PR}-\mathrm{QR}}{2}

=\frac{35+12-37}{2}

=\frac{47-37}{2}=\frac{10}{2}=5

cm.

Answer:

r=5

cm.

Correct option: B. 5 cm.

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