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The length and breadth of a rectangle are in the ratio 4 : 3. Then what is the ratio of the area of the triangle formed by the parts of the diagonals with a long side to the area of the triangle formed by the parts of diagonals with a short side?

The length and breadth of a rectangle are in the ratio 4 : 3. Then what is the ratio of the area of the triangle formed by the parts of the diagonals with a long side to the area of the triangle formed by the parts of diagonals with a short side? Correct Answer 1 : 1

Given:

The length and breadth of a rectangle are in the ratio 4 : 3

Formula Used:

area of triangle = ½ × base × height

Calculation:

Consider the rectangle ABCD shown below,

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Let the length and breadth of the rectangle be ‘4x’ units and ‘3x’ units respectively

⇒ AB = CD = 4x

⇒ BC = AD = 3x

∵ O is the intersection point of diagonals & is the centre of the rectangle,

⇒ OX = AB/2 = 4/2 = 2x

⇒ OY = BC/2 = 3x/2

Now, area of triangle = ½ × base × height

⇒ Area of ∆COD = ½ × CD × OY = ½ × 4x × 3x/2 = 3x2

⇒ Area of ∆BOC = ½ × BC × OX = ½ × 3x × 2x = 3x2

∴ Required ratio = 3x2∶ 3x2 = 1 ∶ 1 

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