Courtney is building a rectangular wading pool.
She wants the area of the bottom to be 54 ft?.
She also wants the length of the pool to be 3 ft
longer than twice its width.
What are the dimensions of the pool?

Dimensions of the pool will be 4.5 ft × 12 ft.

Step-by-step explanation:

Let the width of the pool = x ft

Then length of the pool will be = (2x + 3) ft

Now area of the rectangular pool = Length × width

54 = x(2x + 3)

54 = 2x² + 3x

2x² + 3x - 54 = 0

From quadratic formula,

x =

From the given equation,

a = 2, b = 3 and c = -54

x =

x =

x =

x =

x = 4.5, -6

But x can't be negative, so x = 4.5

Now length of the pool = (2×4.5) + 3 = 12 ft

Width of the pool = 4.5 ft

Therefore, dimensions of the pool will be 4.5 ft × 12 ft

width = 4.5

Length = 12

Step-by-step explanation:

Let w = width

The length is 3 ft longer than 2 times the width

L =2 w+3

The Area is

A = l*w

54 = (2w+3) (w)

Distribute

54 = 2w^2 +3w

Subtract 54 from each side

54-54 = 2w^2 +3w - 54

0 = 2w^2 +3w - 54

Factor

0=(2w-9)(w+6)

Using the zero product property

0 = 2w-9    0 = w+6

2w=9       w=-6

w = 9/2   w = -6

Since we cannot have negative dimensions

w = 9/2

l = 2(9/2) +3  = 9+3  =12

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.