Find the perimeter of a rhombus whose one diagonal is 16 cm long and area is 240 cm2.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 68 cm
The area of a rhombus is half the product of its diagonals, which gives the second diagonal. The diagonals bisect each other at right angles, so half of each diagonal and one side form a right-angled triangle with the side as its longest side.
\(\displaystyle\frac{1}{2}\times16\times d=240\), so the other diagonal \(d=30\) cm
Half-diagonals: 8 cm and 15 cm
Each side, by Pythagoras’ theorem: \(\sqrt{8^2+15^2}=\sqrt{289}=17\) cm
Perimeter, four equal sides: \(4\times17=68\) cm
