Question

if the perimeter of a triangle is 6p+ 10q and the two sides are 6p+ 4q and p+ 3q then find its third side.​

Answer 1

$\sf\small{ \underline{\underline\red{ \pmb{Given:-}}}}$

• Perimeter of triangle: 6p + 10q
• Two sides are 3p + 4q and p + 3q

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$\sf\small{ \underline{\underline\red{ \pmb{ Solve:-}}}}$

• Find the 3ʳᵈ Side

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$\sf\small{ \underline{\underline\red{ \pmb{ Solution:-}}}}$

Add the two sides

Subtract the sum from the perimeter and you will get the 3ʳᵈ side

☆ Adding

ㅤㅤ3pㅤㅤㅤ+ㅤㅤㅤ4q

ㅤㅤ1pㅤㅤㅤ+ㅤㅤㅤ 3q

ㅤ= 4p + 7q

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☆ Subtracting

ㅤ6pㅤㅤ+ㅤㅤ10q

± 4pㅤㅤ±ㅤㅤ7q

= 2p + 3q

$\sf \implies 2p + 3q \: is \: the \: 3rd \: side.$

Answer 2

Given data : The perimeter of a triangle is 6p + 10q and the two sides are 6p + 4q and p + 3q.

Solution :

To find third side;

Here, according to given,

• First side of triangle = 6p + 4q
• Second side of triangle = p + 3q
• Perimeter of triangle = 6p + 10q

Let, third side of triangle be x

• Third side of triangle = x

Now, by formula of perimeter of triangle ;

⟹ Perimeter of triangle = first side + second side + third side

⟹ 6p + 10q = 6p + 4q + p + 3q + x i.e.

⟹ 6p + 10q = 6p + p + 4q + 3q + x

⟹ 6p + 10q = 7p + 7q + x

⟹ x = 6p + 10q - 7p - 7q i.e.

⟹ x = 6p - 7p + 10q - 7q

⟹ x = - p + 3q

Answer : Hence third side of triangle is - p + 3q.

Verification :

⟹ Perimeter of triangle = first side + second side + third side

⟹ Perimeter of triangle = 6p + 4q + p + 3q + (- p + 3q)

⟹ Perimeter of triangle = 6p + 4q + p + 3q - p + 3q i.e.

⟹ Perimeter of triangle = 6p + p - p + 4q + 3q + 3q

⟹ Perimeter of triangle = 6p + 10q

Hence, it verified.