Question

Find the length of the equal sides of the isosceles triangle if the perimeter and unequal are: perimeter = 30cm. unequal side = 8cm​

Answer 1

Answer : 11 cm ( each )

$\rule{100}2$

Given :

• In an isosceles triangle, perimeter = 30 cm ; Unequal side = 8 cm.

To Find :

• The length of equal sides.

Concept :

• In an isosceles Δ, two sides are equal and the third side is unequal. If we take its side ' s ' cm, then the other side will also be ' s ' cm. From this, we can easily find its perimeter, as the magnitude of perimeter is given. Let's do it!

SolUtion :

We know that,

$\sf Perimeter\:of\: \triangle= Sum\:of\:three\:sides$

So, Put the given vales in the formula. we get,

$\sf 30 = s + s + 8$

$\sf\implies 30 = 2s + 8$

$\sf\implies 30-8=2s$

$\sf\implies 22 = 2s$

$\sf\implies s =\dfrac{22}{2}$

$\sf\therefore s = 11$

Hence,

Equal sides of the isosceles Δ are 11 cm ( each ).

$\rule{100}2$

Verification :

By substituting the obtained value of " s " in the formula.

$\sf = 11 + 11 + 8$

$\sf = 30\:cm$

Hence proved!

$\rule{200}2$

Answer 2

Question :

Find the length of the equal sides of the isosceles triangle if the perimeter is 30cm and unequal side is 8cm.

Solution :

$\underline{\bold{Given:}}$

• The length of the unequal side of the isosceles triangle = 8 cm
• Perimeter of the isosceles triangle =30 cm

$\underline{\bold{To\:Find:}}$

• The length of the equal sides of the isosceles triangle .

We know that in an isosceles triangle two sides are equal and one side is unequal.

Let the length of the equal sides be x cm.

$\boxed {\purple{Perimeter \:of\:triangle=Sum \:of \:all\: sides}}$

$\implies 30 =x+x+8\\\implies 30=2x+8\\\implies 30-8=2x\\\implies 22=2x\\\implies \frac {22}{2}=x\\\implies 11=x\\\implies x=11$

$\boxed{\green{\therefore{The\: length\: of\: the\: equal\:sides \:of\: the\:isosceles \:triangle\:is\:11\:cm.}}}$

$\underline{\bold{Verification:}}$

We have :

• The length of the equal sides of the isosceles triangle = 11 cm
• Perimeter = 30 cm

$\implies Perimeter=Sum \:of \:all\: sides\\\implies 30\: cm=11\:cm+11\:cm+8\:cm\\\implies 30\:cm=30\:cm$