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The equal sides of an isosceles triangle are 2 cm shorter than the length of the third side. If the perimeter of the triangle is 35 cm, find the length of the third side.​

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HealingPearl

Given Information :

• Equal sides of an isosceles triangle = 2cm shorter than the length of the third side.

To calculate :

• Length of the third side.

Calculation :

Let the third side be c.

Also, two equal sides be a and b.

According to the question,

[tex] \longmapsto [/tex] a = ( Third side - 2 ) cm

[tex] \longmapsto [/tex] a = ( c - 2 ) cm

Similarly, length of b(second side) will also be same as a and b are two equal sides of an isosceles triangle.

[tex] \longmapsto [/tex] b = ( c - 2 ) cm

Now, we know that :

★ Perimeter of ∆ = Sum of all sides

  • Perimeter = 35 cm.

[tex] \longmapsto [/tex] 35 = a + b + c

[tex] \longmapsto [/tex] 35 = (c - 2) + (c - 2) + c

[tex] \longmapsto [/tex] 35 = c - 2 + c - 2 + c

[tex] \longmapsto [/tex] 35 = c + c + c - 2 - 2

[tex] \longmapsto [/tex] 35 = 3c - 4

[tex] \longmapsto [/tex] 35 + 4 = 3c

[tex] \longmapsto [/tex] 39 = 3c

[tex] \longmapsto [/tex] [tex] \sf \dfrac{39}{3} [/tex] = c

[tex] \longmapsto [/tex] 13 = c

So, third side of the triangle is 13 cm.

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