James is planning on building a swimming pool, enclosed by a baby gate, for his backyard. he knows that he will need a total of 54 feet to completely surround the pool with the gate. when measuring the length and width of the proposed pool area, james discovers that the length is double the width. what are the dimensions of the proposed swimming pool?

the length = 18 feet and width = 9 feet

Step-by-step explanation:

Step 1:

Assume

Length of the rectangle = b

Width of the rectangle = a

Step 2:

As mentioned in the question length is double the width therefore;

b = 2*a

Step 3:

as mentioned in the question James need total 54 feet to cover the pool that means the perimeter of the pool is 54 feet therefore perimeter formula can be used as follows;

P = 2a + 2b

54 = 2a +2(2a) <equation from step 2 has been used for b>

54 = 2a + 4a

54 = 6a

a = 54/6

a = 9 feet

Step 4:

Now again use equation from step b to find out the length;

b =2a

take value of a from step 3

b = 2*9

b = 18 feet

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.