Question

the length of the Unique one side of an isosceles triangle is half the length of one of the equal side if its perimeter is 35 cm find the length of the side of the triangle​

Answer 1

Answer :

The required sides of the triangle are 14cm , 14cm and 7cm

Given :

• The length of the unique one side of an isosceles triangle is half the length of one of the equal side
• The perimeter of the triangle is 35cm

To Find :

• The length of the sides of the triangle

Formula to be used :

$\sf \star \: \: Perimeter \: \: of \: a \: triangle = Sum \: of \: all \: the \: sides \: of \: triangle$

Solution :

Let us consider the sides of the triangle be a , b and c

Let c be the unique sides which is half of the equal sides .

Since the triangle is isosceles

$\sf \dashrightarrow a = b.......(1)$

According to question :

$\sf \dashrightarrow c = \dfrac{a}{2}........(2)$

Now given Perimeter is 35 cm

$\sf \implies a + b + c = 35cm \\\\ \sf \implies a + a + \dfrac{a}{2} = 35 \\\\ \sf \implies 2a + \dfrac{a}{2} = 35 \\\\ \sf\implies \dfrac{4a + a}{2} = 35 \\\\ \sf \implies 5a = 2\times 35 \\\\ \sf \implies a =\dfrac{2\times35}{5} \\\\ \sf \implies a = 2\times 7 \\\\ \sf \implies a = 14cm$

From (1) we have :

$\sf \implies b = 14$

From (2) we have :

$\sf \implies c = \dfrac{14}{2}\\\\ \sf \implies c=7cm$

Therefore, the sides of the triangle are 14cm , 14cm and 7cm