Home
Class 12
MATHS
The sides of a right-angled triangle are...

The sides of a right-angled triangle are integers. The length of one of the sides is 12. The largest possible radius of the incircle of such a triangle is-

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
D

Clearly
`x^(2)-y^(2)=144`
`(x-y)(x+y)=144`
`x,yinI`
So factorsize 144 into two even factors
x+y=72 x+y=36 x+y=18
x-y=2 s-y=9 x-y=8
x=37 x=20 x-13
y=35 y=16 y=5

`r=Delta//s" "r=Delta//s" "r=Delta//s`
`r=(1//2xx12xx35)/(((12+35+37)/(2)))" "r=(1//2xx12xx16)/(((16+20+12)/(2)))" "r=2`
`r=(12xx35)/(84)" "r=(12xx16)/(48)`
`r=5" "r=4`
Promotional Banner

Similar Questions

Explore conceptually related problems

If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by

Find the length of one side of a right angled triangle if the length of one side is 24cm and the radius of the circumcircle is 13cm

The perpendicular sides of a right angled triangle are 3x and 4x . The length of its hypotenuse is 30 . Find the lengths of the perpendicular sides of the right angled triangle.

The length of the two sides of a right-angled triangle are equal Find the length of the hypotenuse

If the length of sides of right angled triangle are in AP, then their ratio is

Two sides of a triangle are in the ratio 3:5 and third side is 16 .If Delta is the largest possible area of the triangle,then Delta=

What is the greatest possible perimeter of a right-angled triangle with integer side lengths if one of the sides has lenth 12?