Ravi is a student of std X. He is drawing a square on a sheet of paper considering each side of the square as 8 cm. Now, he is drawing two equilateral triangles, one by taking side of the square as one of its side and another by taking diagonal of square as sides of another equilateral triangle. Later, few questions came to his mind and he wants to solve them. Give answers to his questions drawing your own figure.
(i) The diagonal of the square is
(a) 8√2 cm
(b) 8√3 cm
(c) 8√5 cm
(d) 8√6 cm
ii) The area of the square is
(a) 64 sq.cm
(b) 81 sq.cm
(c) 121 sq.cm
(d) 49 sq.cm
(iii) The area of an equilateral triangle by taking side of square as sides of triangle is
(a) 8√3 sq.cm
(b) 16√3 sq.cm
(c) 32√3 sq.cm
(d) 24√3 sq.cm(iv) The area of an equilateral triangle by taking diagonal of square as sides of equilateral triangle is
(a) 8√3 sq.cm
(b) 16√3 sq.cm
(c) 32√3 sq.cm
(d) 24√3 sq.cm
Which is true order in area?
(a) Equilateral triangle on side Square > Equilateral triangle with diagonal
(c) Equilateral triangle on diagonal > Equilateral triangle on side > Square
(d) Square >Equilateral triangle on diagonal > Equilateral triangle on side
Answers
Answer:
Hey!
here u go :)
a> option 1
b> option 1
c> option 2
d> option 3
e> option 4
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Given : square of side 8 cm
one equilateral Triangle on side 8 cm
Another equilateral Triangle on diagonal of square
To Find:
i) The diagonal of the square is
(a) 8√2 cm (b) 8√3 cm (c) 8√5 cm (d) 8√6 cm
ii) The area of the square is
(a) 64 sq.cm (b) 81 sq.cm (c) 121 sq.cm (d) 49 sq.cm
(iii) The area of an equilateral triangle by taking side of square as sides of triangle is
(a) 8√3 sq.cm (b) 16√3 sq.cm (c) 32√3 sq.cm (d) 24√3 sq.cm
(iv) The area of an equilateral triangle by taking diagonal of square as sides of equilateral triangle is
(a) 8√3 sq.cm (b) 16√3 sq.cm (c) 32√3 sq.cm (d) 24√3 sq.cm
Which is true order in area?
(a) Equilateral triangle on side Square > Equilateral triangle with diagonal
(c) Equilateral triangle on diagonal > Equilateral triangle on side > Square
(d) Square >Equilateral triangle on diagonal > Equilateral triangle on side
Solution :
The diagonal of the square is √8² + 8² = 8√2
(a) 8√2 cm
The area of the square is 8 x 8 = 64 cm²
(a) 64 sq.cm
(iii) The area of an equilateral triangle by taking side of square as sides of triangle is
(√3/ 4)8² = 16√3 cm²
(b) 16√3 sq.cm
The area of an equilateral triangle by taking diagonal of square as sides of equilateral triangle is
(√3/ 4)(8√2)² =32√3 cm²
(c) 32√3 sq.cm
64 > 32√3 > 16√3
true order in area
Square >Equilateral triangle on diagonal > Equilateral triangle on side
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