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If the diagonals of a rhombus get doubled, then the area of the rhombus becomes ________ its original area

Solution:

The area of the rhombus = Half of the product of its diagonals

Therefore if the diagonals are of length ‘a’ the area of rhombus is:

Area of Rhombus = 1/2 × a × a = (1/2)a²

If the diagonals become ‘2a’ in length then the new area of rhombus is:

New Area of rhombus = 1/2 × 2a × 2a = 2a²

Therefore,

New Area of Rhombus = [2a²]/[a²/2] = 4

Original Area of Rhombus

Hence the new area is 4 times the original area.

✦ Try This: If the diagonals of a rhombus get halved, then the area of the rhombus becomes __________ its original area.

The area of the rhombus = Half of the product of its diagonals

Therefore if the diagonals are of length ‘a’ the area of rhombus is:

Area of Rhombus = 1/2 × a × a = (1/2)a²

If the diagonals become ‘a/2’ in length then the new area of rhombus is:

New Area of rhombus = 1/2 × a/2 × a/2 = a²/8

Therefore,

New Area of Rhombus = [a²/8]/[a²/2] = 1/4

Original Area of Rhombus

Hence the new area is one fourth of the original area.

If the diagonals of a rhombus get halved, then the area of the rhombus becomes one fourth of its original area.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 32

Summary:

If the diagonals of a rhombus get doubled, then the area of the rhombus becomes four times its original area

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