(5+22) x (35-27) + 6^2

The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions

Art [367]

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
$x(2x - 6) = 2 {x}^{2} - 6x$

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

$2 {x}^{2} - 6x = 108$
Subtract 108

$2 {x}^{2} - 6x - 108 = 0$
Divide by 2.

${x}^{2} - 3x - 54$
$(x - 9)(x + 6) = 0$
Rule AB = 0, gives A is 0 or B is 0.

$x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6$

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
$x = 9$
Width
$2x - 6 = 2 \times 9- 6 = 18 - 6 = 12$

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

6 0

3 years ago

78 students are going to be divided into 24 groups and the number of each group member will be either 4 or 2. How many groups of

True [87]

36 and 45 that will be your answer

7 0

3 years ago

Help asap confused on this problem

OverLord2011 [107]

If it’s silver and greater than 1 it would be a quarter

7 0

3 years ago

How do you find the area of a right triangle if you only have the base

valentina_108 [34]

Step-by-step explanation:

You can find the area of a right triangle the same as you would any other triangle by using the following formula:

A = (1/2)bh, where A is the area of the triangle, b is the length of the base and h is the height of the triangle; However, with a right triangle, it's much more convenient in finding its area if we utilize the lengths of the two legs (the two sides that are shorter than the longest side, the hypotenuse and that are perpendicular to each other and thus form the right angle of the right triangle), that is, since the two legs of a right triangle are perpendicular to each other, when we treat one leg as the base, then, consequently, we can automatically treat the length of the other leg as the height, and if we initially know the lengths of both legs, then we can then just plug this information directly into the area formula for a triangle to find the area A of the right triangle.

For example: Find the area of a right triangle whose legs have lengths of 3 in. and 4 in.

Make the 4 in. leg the base. Since the two legs of a right triangle are perpendicular to each other, then the length of the other leg is automatically the height of the triangle; therefore, plugging this information into the formula for the area of a triangle, we have:

A = (1/2)bh

= (1/2)(4 in.)(3 in.)

= (1/2)(12 in.²)

A = 6 in.² (note: in.² means square inches)

8 0

3 years ago

5. Maria is tracking the number of miles she runs in one week. She is using the track at her

777dan777 [17]

Answer:

0.00310 miles

Step-by-step explanation:

Maria runs 5 m each week. We need to find how miles she run. It means we need to convert meters to miles. The relation between meter and yards is as follows :

1 meter = 1.09361 yards

Also, 1 mile = 1760 yards

It means,

1 mile = 1609.34 m

1 m = (1/1609.34) miles

$5\ m=\dfrac{5}{1609.34}\ \text{miles}\\\\=0.00310\ \text{miles}$

So, she will cover 0.00310 miles.

6 0

2 years ago