Question

The perimeter of a triangle is 7p^–8p +9 and two of its sides are 2p^–p +1 and 11p^–3p +5. Find the third side of the triangle.

Answer 1

Answer:

Delta \) AEF \( \equiv \Delta C D F \quad \) ASA Rule So. EF \( = D F \) and \( B E = A E = D C \quad

Step-by-step explanation:

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Answer 2

Given:

• Perimeter of triangle, (P) = $7p^2-8p+9$
• First Side, ($S_1$) = $2p^2-p+1$
• Second side, ($S_2$) = $11p^2-3p+5$

To Find:

• The third side of the triangle.

Solution:

• We know that perimeter of a triangle = Sum of all three sides.
• Let P be the perimeter of the triangle, $S_1$ be the first side and $S_2$ be the second side.
• Let the third side be denoted by "$S_3$".
• We need to find the value of "$S_3$".
• Perimeter, (P) = $S_1$ + $S_2$ + $S_3$
• Substituting the given values,
• ⇒$7p^2-8p+9$ = $2p^2-p+1$ + $11p^2-3p+5$ + $S_3$
• ⇒$7p^2-8p+9$ = $2p^2+11p^2-p-3p+1+5 + S_3$
• ⇒$7p^2-8p+9$ = $13p^2-4p+6+S_3$  
• ⇒$S_3 = 7p^2-8p+9-13p^2+4p-6$
• ⇒$S_3 = -6p^2-4p+3$

∴ The third side of the triangle is $-(6p^2+4p-3)$