Rhombus

Geometry Level 1

one angle of a rhombus is 60 degrees and side = 10cm, find the length of longer diagonal is

6 root 8 54 root 3 10 root 3 9 root 10

Shanthi Jagadeesan by shanthi jagadeesan , 19, India

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1 solution

By cosine rule,

x 2 = 1 0 2 + 1 0 2 − 2 ( 10 ) ( 10 ) cos ⁡ 120 x^2=10^2+10^2-2(10)(10)\cos~120

x 2 = 200 − 200 ( − 1 2 ) x^2=200-200\left(\dfrac{-1}{2}\right)

x 2 = 300 x^2=300

x = 300 = x=\sqrt{300}= 10 3 \boxed{10\sqrt{3}}

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