Question

Find the perimeter of the triangle whose sides are a + b - 3c, - a - b + 6c and 7a - b + 9c​

Answer 1

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Answer 2

Given :

• First side of the triangle = a + b - 3c
• Second side of the triangle = - a - b + 6c
• Third side of the triangle = 7a - b + 9c

To find :

• Perimeter of the triangle

Concept :

Perimeter of any geometric shape is the sum of all its sides.

Mathematically,

• Perimeter of triangle = a + b + c

where,

• a, b and c are the three sides of the triangle

Solution :

Perimeter of the triangle :-

→ Perimeter = a + b + c

Substituting the given values, we get :-

→ Perimeter = a + b - 3c + (- a - b + 6c) + (7a - b + 9c)

→ Removing the brackets and changing the signs.

→ Perimeter = a + b - 3c - a - b + 6c + 7a - b + 9c

→ Perimeter = a - a + 7a + b - b - b - 3c + 6c + 9c

→ Cancelling the variables with the opposite signs.

→ Perimeter = 7a - b - 3c + 6c + 9c

→ Adding the same variables.

→ Perimeter = 7a - b - 3c + 15c

→ Perimeter = 7a - b + 12c

Therefore,

• Perimeter of the triangle whose sides are a + b - 3c, - a - b + 6c and 7a - b + 9c is 7a - b + 12c

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KNOW MORE :

Signs are changed on the following basis :-

• (+) (+) = (+)
• (-) (-) = (+)
• (+) (-) = (-)
• (-) (+) = (-)

Some formulae related to triangles :-

• Semi - perimeter = Perimeter ÷ 2
• Heron's formula = √s(s - a)(s - b)(s - c)
• Area of Isosceles triangle = ½ × b × h
• Area of equilateral triangle = √3/4 a²

where,

• b stands for the base of the triangle
• h stands for the height of the triangle
• a stands for the side of the triangle