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Which of the following statements is/are true? A: If the sides of an equilateral triangle becomes 2√2 times, then its area will become 4√6 times. B: If the distance between any two parallel sides of a rhombus is 25% less than its diagonal, then its other diagonal will be 50% more than its side. C: If ratio between altitude and base of a right-angled triangle is 3: 5, then the ratio between its hypotenuse and base will be √30: 5.

Which of the following statements is/are true? A: If the sides of an equilateral triangle becomes 2√2 times, then its area will become 4√6 times. B: If the distance between any two parallel sides of a rhombus is 25% less than its diagonal, then its other diagonal will be 50% more than its side. C: If ratio between altitude and base of a right-angled triangle is 3: 5, then the ratio between its hypotenuse and base will be √30: 5. Correct Answer Only B

GIVEN:

Three statements.

CONCEPT:

Properties of a triangle and rhombus.

FORMULA USED:

Area of rhombus = a × h = (1/2) × d1 × d2

CALCULATION:

A: If the side of an equilateral triangle is ‘x’, then its area will be √3x2/4

When the side becomes 2√2x, then the new area will be √3 × (2√2x)2/4 = 8√3x2/4.

So, the new area will become 8 times.

B: Let the side of a rhombus is ‘a’, its diagonals are ‘d1’ and ‘d2’ and the distance between any two parallel sides is ‘h’.

So, its area = a × h = (1/2) × d1 × d2

Now,

h = d1 × 75/100 = 3d1/4

⇒ a × 3d1/4 = (1/2) × d1 × d2

⇒ d2 = 3a/2

So, its other diagonal will be 50% more than its side.

C: Let altitude, base and hypotenuse of a right-angled triangle are ‘a’, ‘b’ and ‘c’ respectively.

Since, a: b = 3: 5,

⇒ c = √(a2 + b2) = √ = b√34/5.

So, the ratio between hypotenuse and base is c: b = √34: 5.

Hence, only B is true.

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