Q. 135.0( 2 Votes )

# Prove that the pe

Answer :

Given,

A right angle triangle.

Hypotenuse of the given triangle is given. Let us consider,

‘h’ is the hypotenuse of the given triangle.

‘x’ and ‘y’ be the base and height of the right angle triangle.

The hypotenuse of the ΔABC = AC2 = AB2 + BC2

AC = h, AB = x and BC = y

Hence,

h2 = x2 + y2

y2 = h2 – x2 --- (1)

Now, perimeter of the ΔABC is

P = h + x + y

Now substituting (1) in the area of the triangle, ----- (2)

For finding the maximum/ minimum of given function, we can find it by differentiating it with x and then equating it to zero. This is because if the function f(x) has a maximum/minimum at a point c then f’(c) = 0.

Differentiating the equation (2) with respect to x:   [Since ] ------ (3)

To find the critical point, we need to equate equation (3) to zero.   [squaring on both sides]    [as the base of the triangle cannot be negative.]

Now to check if this critical point will determine the maximum perimeter of the triangle, we need to check with second differential which needs to be negative.

Consider differentiating the equation (3) with x:   [Since if u and v are two functions of x, then ]   Now, consider the value of  As , so the function A is maximum at .

Now substituting in equation (1):  As , the base and height of the triangle are equal, which means that two sides of a right angled triangle are equal,

Hence the given triangle is an isosceles triangle with sides AB and BC equal.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

If the sum of theMathematics - Board Papers

A metal box with Mathematics - Board Papers

Show that aRD Sharma - Volume 1

Find the local maMathematics - Board Papers

Prove that the seMathematics - Board Papers

Prove that the raMathematics - Board Papers

Prove that the leMathematics - Board Papers