The area of a rhombus is 196 sq cm and one of its diagonals is twice the other in length. What is the length of the longer diagonal?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28 cm
The area of a rhombus is half the product of its diagonals, \(\frac{1}{2}d_1d_2\).
Let the shorter diagonal be \(d\); the longer is \(2d\)
\(\displaystyle\frac{1}{2}\times d\times2d=196\), so \(d^2=196\) and \(d=14\) cm
Longer diagonal \(=2\times14=28\) cm
Why the other options are incorrect
Option (1) 14 cm — Incorrect. This is the shorter diagonal, not the longer one.
Option (3) 98 cm — Incorrect. This is half of the area; with diagonals 98 cm and 49 cm the area would be 2401 sq cm.
Option (4) 7 cm — Incorrect. With diagonals 7 cm and 14 cm the area would be only 49 sq cm.