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Q.

The base of a triangle is 80cm and one of the base angles is $60^{0} .$ If the sum of the lengths of the other two sides is 90cm, then the shortest side is

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a

21 cm

b

17 cm

c

15 cm

d

19 cm

answer is D.

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Detailed Solution

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$\begin{array}{rcl} ∠ B & = & 60^{0}, a = 80 \\ b + c & = & 90 \Rightarrow c = 90 - b \\ b^{2} & = & a^{2} + c^{2} - 2 ac cosB \\ b^{2} & = & 6400 + {(90 - b)}^{2} - 2 (80) (90 - b) \frac{1}{2} \\ b^{2} & = & 6400 + 8100 - 180 b + b^{2} - 7200 + 80 b \\ 0 & = & 7300 - 100 b \Rightarrow b = 73 \\ c & = & 90 - 73 = 17 \end{array}$

shortest side 17 cms

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