Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
- The ratios of length : 6 : 7 : 10
- Perimeter of a triangle = 92 cm
Let the lengths of a triangle be 6x , 7x and 10x.
[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
[tex] \underline{ \boxed{ \text{Sum \: of \: all \: sides \: of \: triangle = Perimeter \: of \: a \: triangle}}}[/tex]
⟹ [tex] \sf{6x + 7x + 10 = 92}[/tex]
Solve for x
⟹ [tex] \sf{23x = 92}[/tex]
⟹ [tex] \sf{ \frac{23x}{23} = \frac{92}{23}} [/tex]
⟹ [tex] \sf{x = 4}[/tex] cm
Now , Replacing the value of x :
⟼ [tex] \sf{6x = 6 \times4 = 24}[/tex] cm
⟼ [tex] \sf{7x = 7 \times 4 = 28}[/tex] cm
⟼ [tex] \sf{10x = 10 \times 4 = 40}[/tex] cm
Hence , the sides of the triangle are 24 cm , 28 cm and 40 cm.
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