trinitydg
contestada

A rectangle’s length is 4 more than twice its width. Its area is 240 square centimeters.
Complete the work to find the dimensions of the rectangle.
w(2w + 4) = 240
2w2 + 4w = 240
2w2 + 4w – 240 = 0
2(w + 12)(w – 10) = 0
What is the width of the rectangle? What is the length of the rectangle?

Respuesta :

Since the problem is already factored for you all you have to do is set each of the factor set to zero. Because length cannot be negative, The width is going to be equal to 10cm
Set the equation up no with 10 plugged in for (w) in 240=(l)(10)
Therefore length is 24
 

The length of the rectangle is 24 cm and the width of the rectangle is 10cm.

Given that

A rectangle’s length is 4 more than twice its width.

Its area is 240 square centimeters.

We have to determine

What is the width of the rectangle?

What is the length of the rectangle?

According to the question

Let the length of the rectangle is L

And the width of the rectangle is w.

The area of the rectangle is given by the product of length into width.

[tex]\rm Area \ of \ reactangle = length \times width[/tex]

A rectangle’s length is 4 more than twice its width.

Then, the width of the rectangle is w.

And the length of the rectangle is (2w+4).

Substitute all the values in the formula;

[tex]\rm Area \ of \ rectangle = length \times width\\ \\ 240=(2w+4)\times w\\ \\ 240 = 2w^2+4w\\ \\ 2w^2+4w-240=0\\\\ 2(w^2 + 12w -10w - 10\times 12)=0\\ \\ 2 (w[w + 12] - 10[w + 12] ) = 0\\ \\ 2 (w + 12) (w-10) = 0\\ \\ w+12 =0, \ w=-12\\ \\ w-10=0, \ w=10[/tex]

The width can not be negative so the value of w is 10.

Therefore,

The length of the rectangle is,

2w+4 = 2(10)+4 = 20+4 = 24

Hence, the length of the rectangle is 24 cm and the width of the rectangle is 10cm.

To know more about Rectangle click the link given below.

https://brainly.com/question/14462045

Otras preguntas