Mathematics
The perimeter of a triangle is 8y2 - 9y + 4 and its two sides are 3y2 - 5y and 4y2 + 12. Find its third side.
Algebraic Expressions
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Answer
The perimeter of a triangle = 8y2 - 9y + 4
Two sides are 3y2 - 5y and 4y2 + 12
Let the third side be S.
As we know that, perimeter of triangle = sum of all its side.
8y2 - 9y + 4 = (3y2 - 5y) + (4y2 + 12) + S
⇒ 8y2 - 9y + 4 = 3y2 - 5y + 4y2 + 12 + S
⇒ 8y2 - 9y + 4 = (3y2 + 4y2) - 5y + 12 + S
⇒ 8y2 - 9y + 4 = 7y2 - 5y + 12 + S
⇒ S = (8y2 - 9y + 4) - (7y2 - 5y + 12)
⇒ S = 8y2 - 9y + 4 - 7y2 + 5y - 12
⇒ S = (8y2 - 7y2) + (- 9y + 5y) + (4 - 12)
⇒ S = 1y2 - 4y - 8
Hence, the third side of triangle = (y2 - 4y - 8)
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