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Question

# The area of an isosceles triangle is 60cm2 and the length of each one of its equal sides is 13cm, the length of its base is

A

24 cm, or 20 cm

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B

14 cm, or 10 cm

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C

24 cm, or 10 cm

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D

44 cm, or 10 cm

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Solution

## The correct option is B. 24cm or 10cmLet ABC be an isosceles triangle such that AB=AC=13cmLet BC=2xNow, drop AD⊥BC∴BD=DC [Perpendicular of an isosceles triangle bisects the third side.]⇒BD=DC=2x2=xConsider, right ΔABD, by Pythagoras Theorem,⇒AD2+BD2=AB2⇒AD2+x2=132∴AD2=169−x2...(i)Also, area of ΔABC=60cm2⇒12×BC×AD=60⇒12×2x×AD=60⇒AD=60x...(ii)From (i) and (ii), we get,⇒3600x2=169−x2⇒3600=169x2−x4⇒x4−169x2+3600=0⇒x4−144x2−25x2+3600=0⇒x2(x2−144)−25(x2−144)=0⇒(x2−144)(x2−25)=0⇒x=12,5Therefore, BC=24cm or 10cm.

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