Question

If the perimeter of an isosceles triangle is 11 cm and its unequal side is 5 cm then find its area.







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Answer 1

Let each side of the isosceles triangle be x cm

Then, the perimeter of the triangle is (x+x+5)cm

$= > 11 = x + x + 5 \\ = > 11 - 5 = 2x \\ = > 6 = 2x \\ = > x = \frac{6}{2} \\ = > x = 3cm$

Semi perimeter =

$\frac{11}{2} \: = 5.5cm$

Area of the triangle

$\sqrt{5.5(5.5 - 3)(5.5 - 3)(5.5 - 5)} \\ = \sqrt{5.5 \times 2.5 \times 2.5 \times 0.5} \\ = \sqrt{17.1875} \\ = 4.15sq.cm$

Therefore the are is 4.15sq.cm

Answer 2

Let each side of the isosceles triangle be x cm

Then, the perimeter of the triangle is (x+x+5)cm

\begin{gathered} = > 11 = x + x + 5 \\ = > 11 - 5 = 2x \\ = > 6 = 2x \\ = > x = \frac{6}{2} \\ = > x = 3cm\end{gathered}

=>11=x+x+5

=>11−5=2x

=>6=2x

=>x=

2

6

=>x=3cm

Semi perimeter =

\frac{11}{2} \: = 5.5cm

2

11

=5.5cm

Area of the triangle

\begin{gathered} \sqrt{5.5(5.5 - 3)(5.5 - 3)(5.5 - 5)} \\ = \sqrt{5.5 \times 2.5 \times 2.5 \times 0.5} \\ = \sqrt{17.1875} \\ = 4.15sq.cm\end{gathered}

5.5(5.5−3)(5.5−3)(5.5−5)

=

5.5×2.5×2.5×0.5

=

17.1875

=4.15sq.cm

Therefore the are is 4.15sq.cm