Respuesta :
Answer:
Perimeter of NCAA court=288 feet
Perimeter of new court=259.2 feet
Step-by-step explanation:
We are given that
Length of NCAA court, l=94 feet
Width of NCAA court, b=50 feet
Width of new court, b'=45 feet
We have to find the perimeter of an NCAA court and new court in the school.
Perimeter of NCAA court=[tex]2(l+b)[/tex]
Perimeter of NCAA court=[tex]2(94+50)[/tex]feet
Perimeter of NCAA court=288 feet
When two rectangles are similar then the ration of their corresponding sides are equal.
Using the property
[tex]\frac{Perimeter\;of\;NCAA\;court}{Perimeter\;of\;new\;court}=\frac{Width\;of\;NCAA\;court}{Width\;of\;new\;court}[/tex]
[tex]\frac{288}{Perimeter\;of\;new\;court}=\frac{50}{45}[/tex]
Perimeter of new court=[tex]\frac{288\times 45}{50}[/tex] feet
Perimeter of new court=259.2 feet
The perimeter of the NCAA basketball ground is 288 feet, while the school basketball ground is 259.2 feet.
Given to us,
For NCAA basketball court,
Length, [tex]\bold {L_{NB}}[/tex] = 94 feet,
Width, [tex]\bold {W_{NB}}[/tex] = 50 feet,
For School basketball court,
Width, [tex]\bold {w_{school}}[/tex] = 45 feet,
As discussed in the question, school basketball court will be similar to an NCAA basketball court. Thus, they will be in ratio,
[tex]\bold {\dfrac{L_{NB}}{W_{NB}} = \dfrac{l_{school}}{w_{school}}}[/tex]
Substituting the value,
[tex]\bold {\dfrac{94}{50} = \dfrac{l_{school}}{45}}[/tex]
[tex]\bold{ l_{school} = \dfrac{94\times 45}{50}}[/tex]
[tex]\bold{ l_{school} = 84.6 }[/tex]
We know that, perimeter of rectangular = 2(length+width),
[tex]\begin{aligned}Perimeter_{NB}&= 2(length+width)\\&= 2(94+50)\\&= 288 \end{aligned}[/tex]
[tex]\bold{\begin{aligned}Perimeter_{school}&= 2(length+width)\\&= 2(84.6+45)\\&= 259.2\end{aligned}}[/tex]
Hence, the perimeter of the NCAA basketball ground is 288 feet, while the school basketball ground is 259.2 feet.
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