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=√132−x2=√169−x2 Now, Area =60 cm2 ⇒⇒12(BC×AD)=60 ⇒12{2x×√169−x2}=60 ⇒x√169−x2=60 ⇒x2(169−x2)=3600 ⇒x4−169x2+3600=0 ⇒(x2−144)(x2−25)=0 ⇒x2=144 or, x2=25⇒x=12 or, x=5 Hence, Base = 2x = 24 cm or, 10 cm

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