A wire is first bent into the shape of a rectangle with width 5in and length 13in. Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?

Respuesta :

Total length of the wire = 2*13 + 2*5 = 26 + 10 = 36 in.

so length of each side of the triangle would be 36/3  = 12 ins.

Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].

What is perimeter?

" Perimeter is defined as the total length around the boundary of any two dimensional geomertic shape."

Formula used

Perimeter of a rectangle [tex]= 2 ( L + W)[/tex]

[tex]L =[/tex] length of the rectangle

[tex]W =[/tex] Width of the rectangle

Perimeter of a triangle with equal length [tex]= 3s[/tex]

[tex]s =[/tex] side length of a triangle

According to the question,

Given,

Length of a rectangle [tex]'L'= 13 in[/tex]

Width of a rectangle [tex]'W' = 5 in[/tex]

Substitute the value in the formula we get,

Perimeter of a rectangle [tex]= 2( 13 + 5)[/tex]

                                          [tex]= 36 in[/tex]

Substitute the value in the perimeter of a triangle with equal side length,

[tex]3s = 36 in\\\\\implies s = \frac{36}{3} \\\\\implies s = 12in[/tex]

Hence, Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].

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