Question

side of the triangle are in the ratio of 12:17:25 and its parameter is 540 cm find its area​

Answer 1

Step-by-step explanation:

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$\bf{\bigstar}$ $\text{\Large\underline{\red{Question:-}}}$

:$\Longrightarrow$ ● Side of the triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

$\bf{\bigstar}$ $\text{\Large\underline{\orange{To\ find:-}}}$

:$\Longrightarrow$ ● We have to find the area of the triangle.

$\bf{\bigstar}$ $\text{\Large\underline{\green{Given:-}}}$

:$\Longrightarrow$ ● Ratio of the sides of the triangle = 12 : 17 : 25.

:$\Longrightarrow$ ● Perimeter of the triangle = 540cm.

$\bf{\bigstar}$ $\text{\Large\underline{\purple{Solution:-}}}$

:$\Longrightarrow$ $\mathsf{Let's\ x\ be\ the\ common\ ratio.}$

$\therefore$ $\mathsf{So,\ sides\ of\ triangle\ will\ be\ :\ 12x,\ 17x,\ and\ 25x.}$

:$\Longrightarrow$ $\mathsf{Perimeter\ =\ 540cm.}$

:$\Longrightarrow$ $\mathsf{12x\ +\ 17x\ +\ 25x\ =\ 540cm}$

:$\Longrightarrow$ $\mathsf{54x\ =\ 540cm}$

:$\Longrightarrow$ $\mathsf{x\ =\ \dfrac{540}{54}}$

:$\Longrightarrow$ $\mathsf{x\ =\ 10cm}$ $\red{\bigstar}$

:$\Longrightarrow$ $\mathsf{●\ So,\ the\ sides\ of\ the\ triangle:-}$

:$\Longrightarrow$ $\mathsf{a\ =\ 12x\ =\ 12\ ×\ 10\ =\ 120cm.}$

:$\Longrightarrow$ $\mathsf{b\ =\ 17x\ =\ 17\ ×\ 10\ =\ 170cm.}$

:$\Longrightarrow$ $\mathsf{c\ =\ 25x\ =\ 25\ ×\ 10\ =\ 250cm.}$

:$\Longrightarrow$ $\mathsf{2S\ =\ 540}$

:$\Longrightarrow$ $\mathsf{S\ =\ \dfrac{540}{2}}$

:$\Longrightarrow$ $\mathsf{S\ =\ 270cm.}$ $\green{\bigstar}$

$\bf{\bigstar}$ $\text{\large\underline{\blue{By\ using\ herons\ formula:-}}}$

:$\Longrightarrow$ $\mathsf{Area\ =\ \sqrt{s(s-a)(s-b)(s-c)}}$

:$\Longrightarrow$ $\mathsf{=\ \sqrt{270(270-120)(270-170)(270-250)}}$

:$\Longrightarrow$ $\mathsf{=\ \sqrt{270×150×100×20}}$

:$\Longrightarrow$ $\mathsf\pink{9000cm².}$ $\red{\bigstar}$

$\therefore$ $\fbox{Hence,\ the\ area\ of\ the\ triangle\ is\ 9000cm².}$

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