Question : Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long.
Option 1: 120 cm2
Option 2: 164 cm2
Option 3: 160 cm2
Option 4: 144 cm2
Correct Answer: 120 cm 2
Solution :
The perimeter of a rhombus = 52 cm
One diagonal = 10 cm
Let the length of the other diagonal be $x$ cm.
Perimeter = 4 × side
52 = 4 × side
Side = $\frac{52}{4} = 13$
The diagonals of a rhombus bisect each other at right angles.
Length of other diagonal = $2\sqrt{13^2-(\frac{10}{2})^2}$
$x = 2\sqrt{169-25}$
⇒ $x = 2 × \sqrt{144}$
⇒ $x = 2 × 12 = 24$ cm
⇒ Area of rhombus = $\frac{1}{2}$ × product of diagonals
= $\frac{1}{2}×10×24$
= 5 × 24
= 120 cm
2
Hence, the correct answer is 120 cm
2
.
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