Let shorter diagonal be d, so longer diagonal is 2d. Area of rhombus is (1/2) x d1 x d2 = (1/2) x d x 2d = d². Equating d² = 128 gives shorter diagonal d = √128 = 8√2 cm (approx 11.31 cm).
One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm², find the length of the shorter diagonal.
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Let the length of the shorter diagonal be d cm.
Then the longer diagonal is 2d cm.
The formula for the area of a rhombus is:
Area = (1/2) x diagonal 1 x diagonal 2
Given Area = 128 cm²:
(1/2) x d x 2d = 128
d² = 128
Taking square root on both sides:
d = √128 = √(64 x 2) = 8√2 cm.
In decimal form, 8√2 is approximately 8 x 1.414 = 11.31 cm.
Therefore, the shorter diagonal is 8√2 cm.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/