Question
If an isosceles triangle has a perimeter of 18 cm and base 8 cm, then its area is ___ .
Answer: Option C
:
C
Let each of its equal sides be x.
Then, 2x+8=18 ⇒x=5cm
Hence, the sides are 5cm, 5cm and 8 cm.
Using the Heron's formula,
Area(A)=√s(s−a)(s−b)(s−c)
where s = semi- perimeter and a,b,c are the three sides of the triangle.
Semi−Perimeter(s)=perimeter2
=182 =9cm
A=√9(9−5)(9−5)(9−8)
=√9×4×4×1
=√144cm2
=12cm2
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:
C
Let each of its equal sides be x.
Then, 2x+8=18 ⇒x=5cm
Hence, the sides are 5cm, 5cm and 8 cm.
Using the Heron's formula,
Area(A)=√s(s−a)(s−b)(s−c)
where s = semi- perimeter and a,b,c are the three sides of the triangle.
Semi−Perimeter(s)=perimeter2
=182 =9cm
A=√9(9−5)(9−5)(9−8)
=√9×4×4×1
=√144cm2
=12cm2
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