Find the area of the biggest possible triangle whose base is 10 cm and perimet

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Question

Find the area of the biggest possible triangle whose base is 10 cm and perimeter 36 cm.

Options:

A .

48 c m^{2}

B .

54 c m^{2}

C .

66 c m^{2}

D .

60 c m^{2}

Answer: Option D
:
D
Among all triangles having a specified base and specified perimeter, an isosceles triangle with the specified base has the largest area.
Hence the triangle is isosceles with perimeter 36 cm and base 10 cm.

Each equal side of the triangle -

$= \frac{36 - 10}{2} = 13 c m$
$∴$ Height of the triangle
$= {\sqrt{13}}^{2} - (\frac{10}{2})^{2}$ .
$= \sqrt{169 - 25} = 12 c m$
$∴$ Area of the triangle
$\frac{1}{2} \times 10 \times 12 = 60 c m^{2}$ .

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