If the lengths of the two equal sides of an isosceles triangle are each x cm find the length of the third side so that the triangle has the maximum area. 

Hans007  Feb 10, 2018

I think this happens when the angle between the two equal sides is 90 degrees, or a right-angle isosceles triangle.. Then by Pythagoras' Theorem, you have:

x^2 + x^2 =Hypotenuse^2

2x^2 = Hypotenuse^2 Take the sqrt of both sides

Hypotenuse =x*sqrt(2)

Guest Feb 10, 2018

We can prove the guest's answer as follows :


The area, A, of the triangle can be expressed as


A  = (1/2) x^2 sin (θ )        where θ  is the included angle between the two equal sides


But....the sine is at a maximum at 90°.....so the area is maximized when θ  =  90°



cool cool cool

CPhill  Feb 10, 2018

19 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.