Q28 of 45 Page 1

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum, when the angle between them is 60°.

Let there be a right-angled triangle ABC with ∠ ACB=θ

∠ ABC=90°.



According to the Figure:


AC = h


AB = b


BC = a


Now Area of the triangle


Let h + a = t (as given in the quest)


According to Pythagoras theorem;





Area


=


For area to be maximum should be 0.




t = 3a ….(1)


a + h = t = 3a




θ =60°


Hence proved.


More from this chapter

All 45 →
20

If x = cost(3 - 2 cos2 t) and y = sin t(3 - 2 sin2 t), find the value of at

21

Find the particular solution of the differential equation given that y = 0 when x = 0.

 22

Find the value of p, so that the lines and are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, –4) and parallel to line l1.

 29

Evaluate: