Question

the perimeter of triangle is (17×-12) cm. its two sides are(×-5) cm and (7×+5) cm long. what is the length of third side.​

Answer 1

Appropriate Question :

• The perimeter of triangle is (17x -12) cm. Its two sides are (x-5) cm and (7x+5) cm long. What is the length of third side?

$\sf {\to Answer : (9x - 12) \: cm }$

Given Information :

• Perimeter of triangle = (17x - 12) cm

• Length of two side = (x-5) cm and (7x+5) cm

To calculate :

• Length of the third side.

Calculations :

As we know what,

★ Perimeter of ∆ = Sum of all sides

→ Perimeter = First side + Second side + Third side

→ (17x - 12) = (x - 5) + (7x + 5) + Third Side

→ 17x - 12 = x - 5 + 7x + 5 + Third Side

→ 17x - 12 = x + 7x - 5 + 5 + Third Side

→ 17x - 12 = 8x + Third Side

→ 17x - 8x - 12 = Third Side

→ 9x - 12 = Third Side

Therefore,

• Length of third side is (9x - 12) cm.

Verification :

★ Perimeter of ∆ = Sum of all sides

L.H.S ::

→ (17x - 12) cm

R.H.S ::

→ (x - 5) cm + (7x + 5) cm + (9x - 12) cm

→ (x - 5 + 7x + 5 + 9x - 12) cm

→ (x + 7x + 9x -5 + 5 - 12) cm

→ (17x + 0 - 12) cm

→ (17x - 12) cm

Therefore, L.H.S = R.H.S. Hence, verfied!

Answer 2

Given :

• Perimeter of Triangle = (17x - 12)cm
• 1st side of Triangle = (x - 5)cm
• 2nd side of Triangle = (7x + 5)cm

To Find :

• 3rd side of the Triangle

Solution :

We know that,

⠀⠀★ Perimeter = Sum of all the Sides

⟶⠀Perimeter = Sum of all the Sides

⟶⠀17x - 12 = (x - 5) + (7x + 5) + 3rd side

⟶⠀17x - 12 = x - 5 + 7x + 5 + 3rd side

⟶⠀17x - 12 = x + 7x - 5 + 5 + 3rd side

⟶⠀17x - 12 = x + 7x + 3rd side

⟶⠀17x - 12 = 8x + 3rd side

⟶⠀17x - 8x = 12 + 3rd side

⟶⠀9x = 12 + 3rd side

⟶⠀9x - 12 = 3rd side

So, Third Side of the Triangle is 9x - 12

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More About Triangles :

• A triangle has four vertices
• A triangle has three edges
• A triangle has three sides
• A triangle has three angles
• The sum of angle of a triangle is equal to 180⁰
• Perimeter of triangle = Sum of all sides
• Area of triangle = 1/2 × base × height
• Area of triangle (heron's formula) = √s(s- a) (s - b) (s -c)
• Semi perimeter of triangle = a+b+c/2
• Triangle is closed and 2D shape
• Equilateral triangle, scalene triangle and isosceles triangle are different types of triangles according to their sides
• Acute triangle, right triangle and obtuse triangle are different types of triangles according to their angles
• A triangle is also a polygon

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