The perimeter of a triangle is $7 p q - 2 p + 6$ units and the length of two of its sides are $2 p q - 2 p + 3$ units and $3 p q - 5 p + 2$ units. Find the length of the third side of the triangle.

(2 p q + 5 p + 1)

units

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(p q + 5 p + 1)

units

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(2 p q - 5 p + 1)

units

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(2 p q + p + 1)

units

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Solution

The correct option is A $(2 p q + 5 p + 1)$ units
Let the length of the third side of the triangle be $x$ units.
Given that the perimeter of the triangle is $7 p q - 2 p + 6$ units.
$∴$ Perimeter of the triangle = Sum of the sides of the triangle
$\Rightarrow 7 p q - 2 p + 6 = (2 p q - 2 p + 3) + (3 p q - 5 p + 2) + x$
Grouping the like terms together, we get
$7 p q - 2 p + 6 = (5 p q - 7 p + 5) + x .$
$\Rightarrow x = (7 p q - 2 p + 6) - (5 p q - 7 p + 5)$
$\Rightarrow x = 2 p q + 5 p + 1$
So, the length of the third side of the triangle is $(2 p q + 5 p + 1)$ units.

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