Question

the perimeter of triangular is 540 m and its sides are 25:17:12 find the measurement each of its sides.​ answer by only. appretiance moderator​

Answer 1

Question :-

The perimeter of triangle is 540 m and its sides are in the ratio 25 : 17 : 12. Find the measurement of each of its sides.

$\large\underline{\sf{Solution-}}$

Given that,

The sides of a triangle are in the ratio 25 : 17 : 12.

Let assume that

First side of a triangle = 25x m

Second side of a triangle = 17x m

Third side of a triangle = 12x m

Further given that

Perimeter of triangular figure = 540 m

We know, Perimeter of a triangle is sum of all the three sides of a triangle.

So,

$\rm \: 25x + 17x + 12x = 540$

$\rm \: 54x = 540$

$\rm \: x = \dfrac{540}{54}$

$\rm\implies \:x = 10$

Hence,

First side of a triangle = 25x = 25 × 10 = 250 m

Second side of a triangle = 17x = 17 × 10 = 170 m

Third side of a triangle = 12x = 12 × 10 = 120 m

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

$\begin{gathered} \bold{Question:} \\ \end{gathered}$

the perimeter of triangular is 540 m and its sides are 25:17:12 find the measurement each of its sides.

$\large{\boxed{\tt{\colorbox{pink}{Solution:-}}}}\:$

$\large\blue{\sf{Given:}}$

• Perimeter= 540 m
• Let the sides be; 25x,17x,12x

$\large\color{gold}{ \sf{To\:find}}$

Measurement of each side=?

↬Step by step:

• As we know

$\begin{gathered}\\ \tt{:}\dashrightarrow Perimeter =Sum\:of\:all\:sides\end{gathered}$

• Putting values!

$\begin{gathered}\\ \sf\longmapsto 540=25x+17x+12x\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 540=54x\end{gathered}$

$\large\red{\boxed{\tt{{x=10}}}}\:$

⇰Now,

$\begin{gathered} \bold{⟴\:Side\:1=25x} \\ \end{gathered}$

$\large{|\underline{\mathtt{\red{2}\blue{5}\orange{×}\pink{1}\blue{0}\purple{=}\green{2}\red{5}\blue{0}\orange{}}}}$

$\begin{gathered} \bold{⟴\:Side\:2=17x} \\ \end{gathered}$

$\large{|\underline{\mathtt{\red{1}\blue{7}\orange{×}\pink{1}\blue{0}\purple{=}\green{1}\red{7}\blue{0}\orange{}}}}$

$\begin{gathered} \bold{⟴\:Side\:3=12x} \\ \end{gathered}$

$\large{|\underline{\mathtt{\red{1}\blue{2}\orange{×}\pink{1}\blue{0}\purple{=}\green{1}\red{2}\blue{0}\orange{}}}}$

☣The sides of triangle are 250, 170& 120 respectively..