Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: Upto college level


A rectangle is inscribed in an isosceles triangle with base 1 unit and height h units. what should be the height of the triangle, so that it has minimum area?

6 years ago

Answers : (1)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
There is some correction in question. The rectangle cant have any minimum area. We will find out the maximum area.
Let the triangle be ABC with BC on the x axis and point A on y axis.
A(0,h) B(-1/2,0) C(1/2,0)
Say the rectangle be EFGH with EF side on side BC.
E(-x,0) F(x,0) G(x,y) H(-x,y)
Now the points A G and C lie on same line. Hence, from slope
-2h = y/(x-1/2)
y = h - 2hx
Now the area of rectangle A = 2xy = 2xh(1-2x)
Differentiate it : 2h( 1 - 4x) = 0
Hence, x = 1/4, y = h/2
These are the conditions for the maximum area by rectangle. The question is incomplete. Hence, these are the final answers.

Bharat Bajaj
IIT Delhi
askiitians faculty
6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details