Question

Two equal sides of a triangle are each 5 metres less than twice the third side .If the perimeter of the triangle is 55 Find the length of its side.​

Answer 1

Step-by-step explanation:

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Answer 2

Solution :

$\underline{\bf{Given\::}}}$

• Two equal side of triangle = (2r-5) m
• Third side of triangle = r m
• The perimeter of triangle = 55 m

$\underline{\bf{Explanation\::}}}$

Diagram :

$\setlength{\unitlength}{1.8cm}\begin{picture}\thicklines\put(8,1){\line(1,0){3}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8,1){\line(1,1){1.5}}\put(11,1){\line(-1,1){1.5}}\put(8.1,1.8){\sf{(2r-5)m}}\put(10.3,1.8){\sf{(2r-5)m}}\put(9.3,0.75){\sf{r\:m}}\end{picture}$

We know that formula of the perimeter of triangle :

$\boxed{\bf{Perimeter=Side+Side+Side}}}$

$\longrightarrow\sf{55=(2r-5)+(2r-5)+r}\\\\\longrightarrow\sf{55=2r-5+2r-5+r}\\\\\longrightarrow\sf{55=5r-10}\\\\\longrightarrow\sf{5r=55+10}\\\\\longrightarrow\sf{5r=65}\\\\\longrightarrow\sf{r=\cancel{65/5}}\\\\\longrightarrow\bf{r=13\:m}$

Thus;

$\bullet\:\sf{1^{st}\:Side\:of\:triangle=(2r-5)m=[2(13)-5]m=[26-5]m=\boxed{\bf{21m}}}}\\\\\bullet\sf{2^{nd}\:Side\:of\:triangle=(2r-5)m=[2(13)-5]m=[26-5]m=\boxed{\bf{21m}}}}\\\\\bullet\sf{3^{rd}\:Side\:of\:triangle=(r) m=\boxed{\bf{13m}}}}$