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

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Solution

Logic : 1 Mark
Steps : 2 Marks
Result : 1 Mark

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

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

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

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

$3^{r d} s i d e = 2 p^{2} + 3 p + 5$

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

Logic : 1 Mark Steps : 2 Marks Result : 1 Mark Perimeter of the triangle = sum of the sides of the triangle 6p2−4p+9=p2−2p+1+3p2−5p+3+3rd side 3rd side=6p2−4p+9−[(p2−2p+1)+(3p2−5p+3)] 3rd side=6p2−4p+9−(4p2−7p+4) 3rd side=2p2+3p+5

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