Respuesta :
The question is
What are the dimensions of the original rectangle?
Step 1
Find the scale factor
we know that
The scale factor is equal to
[tex]scale\ factor=\frac{Perimeter\ original \ rectangle}{Perimeter\ reduced\ rectangle}[/tex]
we have
[tex]Perimeter\ original \ rectangle=120\ m[/tex]
[tex]Perimeter\ reduced \ rectangle=30\ m[/tex]
Substitute the values
[tex]scale\ factor=\frac{120}{30}=4[/tex]
therefore
the scale factor is [tex]4[/tex]
Step 2
Find the width of the reduced rectangle
we know that
The perimeter of a rectangle is equal to
[tex]P=2L+2W[/tex]
where
L is the length side of the rectangle
W is the width side of the rectangle
Reduced rectangle
we have
[tex]L=9\ m[/tex]
[tex]P=30\ m[/tex]
substitute
[tex]30=2*9+2W[/tex]
[tex]30=18+2W[/tex]
Solve for W
[tex]2W=30-18[/tex]
[tex]W=12/2=6\ m[/tex]
therefore
The dimensions of the reduced rectangle are [tex]9\ m\ *\ 6\ m[/tex]
Step 3
Find the dimensions of the original rectangle
Original Length
we know that
[tex]original\ length=scale\ factor*reduced\ length[/tex]
we have
[tex]reduced\ length=9\ m[/tex]
[tex]scale\ factor=4[/tex]
substitute
[tex]original\ length=4*9=36\ m[/tex]
Original Width
we know that
[tex]original\ width=scale\ factor*reduced\ width[/tex]
we have
[tex]reduced\ width=6\ m[/tex]
[tex]scale\ factor=4[/tex]
substitute
[tex]original\ width=4*6=24\ m[/tex]
therefore
The dimensions of the original rectangle are [tex]36\ m\ *\ 24\ m[/tex]
The length of the original rectangle is 36 meters and the width is 24 meters.
What is scaled diagram?
A scaled diagram is a reduced form in terms of dimensions of an original image / building / object.
Scale of the drawing = original dimensions / dimensions of the scale drawing
= 120 / 30
= 4
What are the dimensions of the original rectangle?
Length = 9 x 4 = 36 meters
Width = (perimeter / 2) - length
= (120 / 2) - 36
= 60 - 36
= 24 meters
To learn more about a rectangle, please check: https://brainly.com/question/16595449
