Question

2. The length of the sides of a triangle are in the ratio 4 : 5:6 and its perimeter is 150 em,
Find (i) the area of the triangle11) the height corresponding to the longest side,

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Answer 1

Answer:-

Let us Consider that the sides of the Triangle are $\bf{4x, 5x \: and \: 6x}$.

• Given:-

Perimeter of Triangle =$\bf{150m}$

• Solution:-

$\longrightarrow\sf 4x + 5x + 6x = 150$

$\longrightarrow\sf 15x = 150$

$\longrightarrow\sf x = \dfrac{150}{15}$

$\implies\bf{x \:=\: 10}$

Sides of the Triangle:

$\longrightarrow\sf 4x = 4(10)$

$\implies\bf{40}$

$\longrightarrow\sf 5x = 5(10)$

$\implies\bf{50}$

$\longrightarrow\sf 6x = 6(10)$

$\implies\bf{60}$

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Now,Using Heron's Formula:-

$\large{\boxed{\bf{\sqrt{s(s\:-\:a) (s\:-\:b) (s\:-\:c)}}}}$

$\longrightarrow\sf s = \dfrac{a\:+\:b\;+\:c}{2}$

$\longrightarrow\sf s = \dfrac{150}{2}$

$\implies\bf{s = 75}$

Here::

$\bf{s \: = \: 75} \\ \bf{a \:=\: 40} \\ \bf{b\:=\: 50} \\ \bf{c\:=\: 60}$

$\longrightarrow\sf \sqrt{75(75 - 40) (75 - 50) (75 - 60)}$

$\longrightarrow\sf \sqrt{75(35) (25) (15)}$

$\longrightarrow\sf\sqrt{984375}$

$\longrightarrow\bf{992.15}$

Area of Triangle is $\bf{992 cm^2}$

Now, Height corresponding to the longest side :

$\longrightarrow\sf \dfrac{ 2 \times 992}{60}$

$\implies\large\bf{33.07 \:cm}$

Hence,the Height corresponding to the longest side is 33.07 cm.

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