Question

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.​

Answer 1

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=$2(l+b)$

Perimeter of NCAA court=$2(94+50)$feet

Perimeter of NCAA court=288 feet

When two rectangles are similar then  the ration of their   corresponding sides are equal.

Using the  property

$\frac{Perimeter\;of\;NCAA\;court}{Perimeter\;of\;new\;court}=\frac{Width\;of\;NCAA\;court}{Width\;of\;new\;court}$

$\frac{288}{Perimeter\;of\;new\;court}=\frac{50}{45}$

Perimeter of new court=$\frac{288\times 45}{50}$ feet

Perimeter of new court=259.2 feet