Question

An isosceles triangle has a base of 6 units, and an area of 36 square units. Find the dimensions of the largest rectangle that can be placed inside the triangle, with one of the sides at the base of that triangle.

Answer 1

Solution: Base of isosceles triangle - 6 units Bc A = I base x height = 36 * x 6 x height = 36 height = 12 units = AD BD = + x6 =3 units - CD T {property of J 2 el let rectangle of G H length al, breadthab EH = fad Efath=b [IE D = Df=b/2 fc = DC-Df' = 3-1/2 Area of rectangle Aalib B fig

Using the property of similar triangle in Similar o ADC and safe AD 1] fo fo 3 12 I Z-b/a V 12 e 6-b * 266-b) l I 12-2b Putting value A = 42-2b) b class I in egress, we get of دان + A = 126-262 Diffesentiating equals wir to be both sides da = 12-46 iv) for max or min do 20 > 20 12~46 = 0 ab a b=3 ad alla =-4 (re) maxima (largest rectangle) Putting value of b in egin ni d = 12 - 2x3 = 6 Dimension of largest rectangle are Length I= 6 units Breadth b = 3 units