What is the greatest possible perimeter of a right angeled triangle with integer sides lengths if one of the sides has length 12?
Asked by vikasg13.hardware | 13th Jun, 2018, 12:01: PM
Expert Answer:
According to the triangle inequality,
Let x and y be the sides of the triangle
x + y > 12 and x - y < 12
One of the side of the triangle is 12 cm
x2 + 122 = y2
x2 - y2 = 144
x = 13 and y = 5 OR x = 37 and y = 35 Satisfies all the three equations.
The greatest possible perimeter is 12 + 35 + 37 = 84 cm
Answered by Sneha shidid | 13th Jun, 2018, 04:41: PM
Concept Videos
- show that in a right angle triagle the hypotenuse is the longest side
- Prove that the perimeter of a triangle is greater than the sum of its three medians.
- Prove that if two sides of a triangle are unequal, the longer side has greater angle opposite it.
- In the figure PQ > PR, QS and RS are the bisectors of
Q and R respectively. Prove that SQ > SR. 
- Prove that the sum of the three altitudes of a triangle is less than the sum of the three sides of the triangle.
- In the figure AD is the bisector of
A, prove that AB > BD.
- In the given figure, x > y. Show that LM > LN.
- Prove that in a right triangle, the hypotenuse is the longest side.
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change