Question

the perimeter of an isosceles triangle is 10 3/4 cm if one of it's equal sides is 2 5/6 cm ,find The third side.

Answer 1

The perimeter of an isosceles triangle = 10–3/4 or we can also write 43/4 cm

If one of the equal sides is 2–5/6 or 17/6 cm

then the third side will be = 43/4 -34/6 

                                       = (258–136)/24 

                                       = 122/24 

                                       = 5–1/12 cm.

Answer 2

Answer: The third side is $5\dfrac{1}{12}\ cm$.

Step-by-step explanation:

Since we have given that

Perimeter of an isosceles triangle = $10\frac{3}{4}\ cm=\frac{43}{4}\ cm$

Since we know that isosceles triangle has two equal sides and one non equal side.

So, One of its equal sides = $2\frac{5}{6}\ cm=\frac{17}{6}$

Let the third side be 'x'.

According to question,

Perimeter of isosceles triangle = 2s+x = $\frac{43}{4}$

$2\times \dfrac{17}{6}+x=\dfrac{43}{4}\\\\\dfrac{17}{3}+x=\dfrac{43}{4}\\\\x=\dfrac{43}{4}-\dfrac{17}{3}\\\\x=\dfrac{43\times 3-17\times 4}{12}\\\\x=\dfrac{129-68}{12}\\\\x=\dfrac{61}{12}\\\\x=5\dfrac{1}{12}\ cm$

Hence, the third side is $5\dfrac{1}{12}\ cm$