Question

Question 34

The perimeter of a triangle is 28 cm. One of it's sides is 8 cm. Write all the sides of the posible isosceles triangles with these measurements.

Answer 1

Given, perimeter of triangle = 28 cm

and one side = 8 cm

Let the other sides be of length 'a' cm.

$\because$ In isosceles triangle, two sides are equal

$\therefore$ The other side will be $a$ only

According to the question,

Perimeter of triangle = Sum of its all sides

$\Rightarrow$ 28 = 8 + a + a

$\Rightarrow$ 28 = 8 + 2a

$\Rightarrow$ 28-8= 2a

$\Rightarrow$ 20 = 2a [Transposing 8 to LHS ]

$\Rightarrow \frac{20}{2}=\frac{2a}{2}$ [dividing both sides by 2]

$\Rightarrow$ a = 10

Hence, sides are 8 cm, 10 cm and 10 cm.

Again, let two equal sides be 8 cm and 8 cm

and third side = a

Now, according to the question,

Perimeter of triangle = Sum of its all sides

$\Rightarrow$ 28 = 8 + 8+ a

$\Rightarrow$ 28 = 16 + a

$\Rightarrow$ 28-16 = a [transposing 16 to LHS]

$\Rightarrow$ 12 = a

Hence, sides are 8 cm, 8 cm and 12 cm.