Question

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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Answer 1

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,

$\longmapsto$ a = ( Third side - 2 ) cm

$\longmapsto$ 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.

$\longmapsto$ b = ( c - 2 ) cm

Now, we know that :

★ Perimeter of ∆ = Sum of all sides

• Perimeter = 35 cm.

$\longmapsto$ 35 = a + b + c

$\longmapsto$ 35 = (c - 2) + (c - 2) + c

$\longmapsto$ 35 = c - 2 + c - 2 + c

$\longmapsto$ 35 = c + c + c - 2 - 2

$\longmapsto$ 35 = 3c - 4

$\longmapsto$ 35 + 4 = 3c

$\longmapsto$ 39 = 3c

$\longmapsto$ $\sf \dfrac{39}{3}$ = c

$\longmapsto$ 13 = c

So, third side of the triangle is 13 cm.