Question

What is the area of the largest equilateral triangle that can be constructed inside a rectangle of dimensions 20 cm x 10 cm?

Answer 1

The biggest triangle you can fit within the rectangle is one that has its base identical to one of the sides of the rectangle and the third vertex lies on the opposite side - i.e. its area is lw/2. Anything other than this is sub-optimal. To understand this, consider △EKC in the diagram below.

Area of △EKI is half that of rectangle AEIG

.

Area of △EJI

is less than half that of rectangle EBHI

.

Area of △IJC

is again less than half that of rectangle IHCF.

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