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Question

The area of an isosceles triangle is 60 cm2 and the length of each one of its equal sides is 13 cm. Find its base.
[4 MARKS]


Solution

Framing of equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark



Let ABC be the given isosceles triangle in which AB = AC = 13 cm. Draw AD perpendicular from A on BC.

Let BC=2x cm. Then, BD=DC=x cm

In ΔABD, we have

AB2=AD2+BD2                      [By Pythagoras Theorem]

132=AD2+x2

AD=132x2=169x2

Now, Area =60 cm2

12(BC×AD)=60

12{2x×169x2}=60

x169x2=60

x2(169x2)=3600

x4169x2+3600=0

(x2144)(x225)=0

x2=144 or, x2=25x=12 or, x=5

Hence, Base = 2x = 24 cm or, 10 cm

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