If the sum of the lengths of the diagonals of a rhombus of side 4cm is 10cm. What is its area?
8cm2
9cm2
10cm2
12cm2
A
9cm2
B
10cm2
C
12cm2
D
8cm2
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Solution
Verified by Toppr
Let d1 and d2 be the lengths of the diagonals of the rhombus. Then, (d12)2+(d22)2=42⇒d224=16 ⇒d21+d22=64 ⇒(d1+d2)2−2d1d2=64 ⇒102−2d1=100−64(∴d1+d2=10) ⇒2d1d2=100−64=36 ⇒d1d2=18⇒12d2d2=9cm2 ∴ Area of the rhombus =9cm2
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