Maths-
General
Easy
Question
A square and equilateral triangle have equal perimeters. If the diagonal of the square is 12 cm, find the area of triangle.
Hint:
Use Pythagoras theorem to find side of the square.
The correct answer is: 110.85 cm2
It is given that diagonal of the square = 12 cm
Using Pythagoras theorem in triangle ACD
AD2 = AC2 + CD2
(12)2 = x2 + x2 = 2x2
288 = 2x2
144 = x2
12 = x
So, side of the square = 12 cm
Let side of an equilateral triangle = a
Perimeter of triangle = Perimeter of square
⇒ 3a = 4(side) = 4(12) = 48 cm
⇒ a = 16 cm
Now, Area of an equilateral triangle = a2
= 162 = 64
( = 1.73)
= 110.85 cm2
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