Sum of the diagonals of a rhombus is 46 cm. Side of the rhombus is 17 cm. What is the area (in square cm) of the rhombus?
Show answer & explanation
Correct answer: A
Explanation
Let the diagonals be d1 and d2.
d1 + d2 = 46
Side of the rhombus = 17 cm
The diagonals bisect each other at right angles.
Let -
d1/2 = x and d2/2 = y
x + y = 23
x² + y² = 17² = 289
(x + y)² = x² + y² + 2xy
23² = 289 + 2xy
529 = 289 + 2xy
2xy = 240
Area = d1 × d2 / 2
= (2x × 2y)/2
= 2xy = 240 sq cm