First slide

Cartesian plane

Question

If one side of a rhombus has endpoints $(4, 5)$ and $(1, 1)$ , then the maximum area of the rhombus is

Moderate

A

50 sq. units
B

25 sq. units
C

30 sq. units
D

20 sq. units

Solution

From the figure,
Area of rhombus $= 2 \times (Area of ΔABD)$
$= 2 \times \frac{1}{2} \times 5 \times 5 sinθ$
$25 sinθ$
Hence, the maximum area is 25 ( when $sinθ = 1$ ).

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