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.
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)
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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