Answer :
The perimeter of a rectangle is 37 units.
A rectangle is a quadrilateral. It has four angles. All the angles in a rectangle are equal. The perimeter of a rectangle is
p ( rectangle ) = 2 ( l + w ) → 1
where, l = length of the rectangle
w = width of the rectangle
As per the given question, the coordinates of a rectangle are A ( 1, 7 ), B ( 8, 7 ), C ( 8, -3 ) and D ( 1, -3 ).
To find the length and width of the rectangle i.e. the length of each side, we use the distance formula.
Distance = [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex] → 2
- length of the rectangle = AB = DC
- width of the rectangle = AD = BC
AD ⇒ [tex]{(x_{1}, y_{1}) }[/tex] = ( 1, 7 ) and [tex]{(x_{2}, y_{2}) }[/tex] = ( 1, -3 )
Substitute the values in 2,
AD = [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
= [tex]\sqrt{(1-1)^{2} + (7 - (-3))^{2} }[/tex]
= [tex]\sqrt{(0)^{2} + (10)^{2} }[/tex]
= [tex]\sqrt{0+ (10)^{2} }[/tex]
= [tex]\sqrt{(10)^{2} }[/tex]
AD = 10
∴ Width of the rectangle ( w ) = AD = BC = 10 units
AB ⇒ [tex]{(x_{1}, y_{1}) }[/tex] = ( 1, 7 ) and [tex]{(x_{2}, y_{2}) }[/tex] = ( 8, 7 )
Substitute the values in 2,
AB = [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
= [tex]\sqrt{(1-8)^{2} + (7 - 7)^{2} }[/tex]
= [tex]\sqrt{(-7)^{2} + (0)^{2} }[/tex]
= [tex]\sqrt{(7)^{2} + 0 }[/tex]
= [tex]\sqrt{(7)^{2} }[/tex]
AB = 7
∴ Length of the rectangle ( l ) = AB = DC = 7 units
Substitute the values l = 10 and w = 7 in 1,
⇒ p ( rectangle ) = 2 ( l + w )
= 2 ( 7 + 10 )
= 2 ( 17 )
p ( rectangle ) = 34
Therefore, the perimeter of the rectangle with the coordinates A ( 1, 7 ), B ( 8, 7 ), C ( 8, -3 ) and D ( 1, -3 ) is 34 units.
To know more about finding the perimeter of a rectangle refer to:
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