Question

14 m, find
10. Two equal sides of an isoscles triangle are each 2 cm more than thrice the third side.
the perimeter of triangle is 67 cm, find the lengths of its sides.​

Answer 1

Given :

• Two Equal side of the isosceles triangle = 3(Third side) + 2 cm.

• Perimeter of the triangle = 67.

To find :

Length of all sides of the triangle.

Solution :

Let the third side of the triangle be x.

So According to the Question ,

Equal sides of the triangle = 3(Third side) + 2 cm.

By Substituting the value of third side (in terms of x) in the equation, we get :

==> Equal Sides = (3x + 2) cm.

So here we get the three sides of the triangle as :

• a = 3x + 2
• b = 3x + 2
• c = x

Now ,

we know the formula for Perimeter of a triangle ,i.e,

Perimeter of a triangle = Sum of all the sides

or,

⠀⠀⠀⠀⠀⠀⠀⠀⠀P = a + b + c

Where :

• P = Perimeter of the triangle
• a , b and c = Sides of the triangle

Now by using the formula for perimeter of a triangle and substituting the values in it, we get :

==> P = a + b + c

==> 67 = (3x + 2) + (3x + 2) + x

==> 67 = 3x + 2 + 3x + 2 + x

==> 67 = (3x + 3x + x) + (2 + 2)

==> 67 = 7x + 4

==> 67 - 4 = 7x

==> 63 = 7x

==> 63/7 = x

==> 9 = x

∴ x = 9 cm.

Hence the value of x is 9 cm.

Now , let's find out the Sides of the triangle :

• First side of the triangle :

==> a = 3x + 2

By Substituting the value of x in the equation , we get :

==> a = (3 × 9) + 2

==> a = 27 + 2

==> a = 29.

∴ a = 29 cm.

Hence the first Side of the triangle is 29 cm.

• Second side of the triangle :

==> b = 3x + 2

By Substituting the value of x in the equation , we get :

==> b = (3 × 9) + 2

==> b = 27 + 2

==> b = 29.

∴ a = 29 cm.

Hence the first Side of the triangle is 29 cm.

• Third side of the triangle :

==> c = x

By By Substituting the value of x in the equation , we get :

==> c = 9

∴ c = 9 cm.

Hence the third Side of the triangle is 29 cm.

Answer 2

Answer:

9cm,29cm,9cm

Step-by-step explanation:

Let thrid side = x,

According to the question ,

the equal sides are = 2+3x

We know perimeter of the triangle is 67cm

meaning ,

x+(2+3x)+(2+3x) = 67

x+2(2+3x) = 67

x+4+6x=67

7x+4=67

7x=67-4

7x=63

x=63/7

x=9

Therefore, the thrid side = 9cm

the equal sides = 2+3*9 = 2+27

= 29cm

________________________________

extra step to cross check the answer,

perimeter of ∆ = 67cm

so if we add all sides of ∆ i.e, 9cm,29cm & 29cm,

it should be 67cm

let's add 9+29+29=67,

thus, the answer is correct.

________________________________

peace ✌️