Question

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

• A. ($p^2-5p+1$) units
• B. ($2p^2+5p-1$) units
• C. ($2p^2+5p+1$) units
• D. ($p^2-5p-1$) units

Answer 1

The correct option is C ($2p^2+5p+1$) units

Let the length of the third side of the triangle be x units.
Given that,
Perimeter of the triangle = $7p^2-2p+6$ units
$\therefore$ Perimeter of the triangle = Sum of the sides of the triangle
$\Rightarrow 7p^2-2p+6=(2p^2-2p+3)+(3p^2-5p+2)+x$
$\Rightarrow (7p^2-2p+6)=(5p^2-7p+5)+x$,
$\Rightarrow x=(7p^2-2p+6)-(5p^2-7p+5)$,
$\Rightarrow x=2p^2+5p+1$.
So, the length of the third side of the triangle
$=2p^2+5p+1$.