Question

the perimeter of an isosceles triangle is 71/2 cm. if the base is 26/2 cm, find the length of each equal sides

Answer 1

GIVEN:

• Perimeter of an isosceles triangle = 71/2 cm
• Base of an isosceles triangle = 26/2 cm

TO FIND:

• What is the length of each equal side ?

SOLUTION:

We have given that, the perimeter of an isosceles triangle is 71/2 cm. if the base(b) is 26/2 cm

Let the length of each equal side be 's' cm

We know that the formula for finding the perimeter of an isosceles triangle is:-

$\bf{\star \: Perimeter = (2s + b)\: \star}$

According to question:-

$\rm{\dashrightarrow \dfrac{71}{2} = \Bigg(2s + \dfrac{26}{2}\Bigg)}$

$\rm{\dashrightarrow \dfrac{71}{2} = \Bigg( \dfrac{4s + 26}{2} \Bigg)}$

$\rm{\dashrightarrow \dfrac{71}{\cancel{2}} \times \cancel{2} = 4s + 26 }$

$\rm{\dashrightarrow 71 - 26 = 4s }$

$\rm{\dashrightarrow 45 = 4s }$

$\rm{\dashrightarrow s = \cancel\dfrac{45}{4}}$

$\bf{\dashrightarrow \star \: s = 11.25 \: cm \: \star}$

❝ Hence, the length of each equal side of an isosceles triangle is 11.25 cm ❞

_____________________

VERIFICATION:

Put the values in the formula:-

➨ $\rm{\dfrac{71}{2} = \Bigg(2\times 11.25 + \dfrac{26}{2}\Bigg)}$

➨ $\rm{\dfrac{71}{2} = \Bigg(22.5 + \dfrac{26}{2}\Bigg)}$

➨ $\rm{ \dfrac{71}{2} = \Bigg(\dfrac{ 45 + 26}{2}\Bigg) }$

➨ $\rm{ \dfrac{71}{2} = \dfrac{71}{2}}$

$\rm{ [L.H.S. = R.H.S.]}$

VERIFIED....