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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 10cm


Let ABC be an isosceles triangle such that AB=AC=13cm

Let BC=2x

Now, drop ADBC

BD=DC [Perpendicular of an isosceles triangle bisects the third side.]

BD=DC=2x2=x

Consider, right ΔABD, by Pythagoras Theorem,

AD2+BD2=AB2

AD2+x2=132

AD2=169x2...(i)

Also, area of ΔABC=60cm2

12×BC×AD=60

12×2x×AD=60

AD=60x...(ii)

From (i) and (ii), we get,

3600x2=169x2

3600=169x2x4

x4169x2+3600=0

x4144x225x2+3600=0

x2(x2144)25(x2144)=0

(x2144)(x225)=0

x=12,5

Therefore, BC=24cm or 10cm.


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