Question

Two equal side of a triangle are 5 m less than twice
the 3 side. If the perimeter of the triangle is 55 m
find the length of its side ?​

Answer 1

$\large{\dag\underline{\pink{\frak{Given:}}}\dag}$

• $\red{\textsf{Two equal sides of Triangle are 5m less than 3side.}}$
• $\blue{\textsf{Perimeter of Triangle is 55m}}$

$\large{\dag\underline{\pink{\frak{Find:}}}\dag}$

• $\purple{\textsf{Length of all sides.}}$

$\large{\dag\underline{\pink{\frak{Solution:}}}\dag}$

Let, the length of the third side be 'x' m

☯ According To Question:-

Other two equal sides are 5m less than twice the 3rd side.

$\sf\implies (2x - 5)m$

Now,

$\sf \mapsto Perimeter \: of \: triangle = sum \: of \: all \: sides$

$\sf where \small{\begin{cases} \sf Perimeter = 55m \\ \sf {3}^{rd} side = x \:m \\ \sf {1}^{st} side = {2}^{nd}side = (2x - 5)m \end{cases}}$

♡Substituting these values:-

$\sf \dashrightarrow Perimeter = {1}^{st} side + {2}^{nd}side + {3}^{rd} side$

$\sf \dashrightarrow 55= 2x - 5 + 2x - 5 + x$

$\sf \dashrightarrow 55= 5x - 5 - 5$

$\sf \dashrightarrow 55= 5x - 10$

$\sf \dashrightarrow 55 +10= 5x$

$\sf \dashrightarrow 65= 5x$

$\sf \dashrightarrow \dfrac{65}{5}= x$

$\sf \dashrightarrow 13m= x$

$\underline{\boxed{ \begin{gathered}\therefore\sf F1^{st} side=2x-5 \\ \sf = 2 \times 13 - 5 \\ \sf = 26 - 5 \\\sf = 21m\end{gathered}}}$

$\underline{\boxed{ \begin{gathered}\therefore\sf 2^{nd} side=2x-5 \\ \sf = 2 \times 13 - 5 \\ \sf = 26 - 5 \\\sf = 21m\end{gathered}}}$

$\underline{\boxed{ \begin{gathered}\therefore\sf 3^{rd} side=x = 13m\end{gathered}}}$

Answer 2

Answer:

Let the third side be x m.

Then the two equal sides are of length (2x−5) m.

Perimeter of triangle = 55 m.

⟹x+(2x−5)+(2x−5)=55

⟹5x−10=55

⟹x=13

Hence, the length of the triangle's sides are 13m, 21m and 21m.