The perimeter of a triangle is $6 p^{2} - 4 p + 9$ and the length of two of its adjacent side are $p^{2} - 2 p + 1$ and $3 p^{2} - 5 p + 3$ . Find the length if the third side of the triangle. If p = 3, find the perimeter of the triangle. [4 MARKS]

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Solution

Forming the equation: 1 Mark
Steps: 1 Marks
Equation for perimeter: 1 Mark
Perimeter: 1 Mark

Perimeter of the triangle = sum of the sides of the triangle

$6 p^{2} - 4 p + 9 = p^{2} - 2 p + 1 + 3 p^{2} - 5 p + 3 + 3^{r d} s i d e$

$3^{r d} s i d e = 6 p^{2} - 4 p + 9 - [(p^{2} - 2 p + 1) + (3 p^{2} - 5 p + 3)]$

$3^{r d} s i d e = 6 p^{2} - 4 p + 9 - (4 p^{2} - 7 p + 4)$

$3^{r d} s i d e = 2 p^{2} + 3 p + 5$
The $3^{r d}$ side of the triangle has length is $2 p^{2} + 3 p + 5$

Given that
p = 3
The perimeter of the triangle is $6 p^{2} - 4 p + 9$ .
On substituting the values we get:
$= 6 \times 3^{2} - 4 \times 3 + 9$
$= 54 - 12 + 9$
$= 51$

The perimeter of the triangle is 51 units.

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The perimeter of a triangle is 6p2−4p+9 and the length of two of its adjacent side are p2−2p+1 and 3p2−5p+3. Find the length if the third side of the triangle. If p = 3, find the perimeter of the triangle. [4 MARKS]

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