QUESTION 5
Easy
One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm\(^2\), find the length of the shorter diagonal.
SOLUTION
Let the shorter diagonal be \(x\) cm.
Then the longer diagonal is \(2x\) cm.
Given,
Area \(= 128\) cm
\(\frac{1}{2} (x)(2x)\,= 128\)
\(x^2 = 128\)
\(x = \sqrt{128}\)
\(x = \sqrt{8^2 × 2 }\)
\(x = 8 \sqrt{2}\)
So, the shorter diagonal is 8√2 cm or approximately 11.3 cm.
Then the longer diagonal is \(2x\) cm.
Given,
Area \(= 128\) cm
\(\frac{1}{2} (x)(2x)\,= 128\)
\(x^2 = 128\)
\(x = \sqrt{128}\)
\(x = \sqrt{8^2 × 2 }\)
\(x = 8 \sqrt{2}\)
So, the shorter diagonal is 8√2 cm or approximately 11.3 cm.
🏆
Final Answer : Length of shorter diagonal = 8√2 cm
Concept Note
The area of a rhombus is given by
\(Area = \frac{1}{2} d_1 d_2\)
where
\(d_1 = first diagonal\)
\(d_2 = second diagonal\)