If the inradius in a right angled triangle with integer sid…

Maths Trigonometrical Equations and in Equations, Properties of Triangles, Height and Distance General Subjective Type

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If the inradius in a right angled triangle with integer sides is r. Prove that

(i) If r = 4, the greatest perimeter (in units) is 90

(ii) If r = 5, the greatest area (in sq. units) is 330

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(i and ii) Let a, b and c (a < b < c) be the sides of given triangle.

Also, 2r = a + b – c

When r = 4 then, (a, b) = (9, 40), (10, 24), (12,16)

∴ Greatest perimeter = 9 + 40 + 41 = 90 units

when r = 5 then (a, b) = (11, 60) (12,35) (15,20)

∴ Greatest area = = 330 sq. unit

──────────────────────────────────────────────────────────────────────────────────────────

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.