Arectangular cardboard sheet has a length that is 1.5 times greater than the width. is it possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet if squares with a side of 8 cm are cut from the corners? find the dimensions of the cardboard sheet.

Yes, it is possible  to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.

The dimensions of the cardboard sheet are 54 cm x 36 cm

Step-by-step explanation:

Let

x ----> the length of the cardboard sheet

y ----> the width of the cardboard sheet

we know that

----> equation A

The volume of the topless box is

where

substitute

----> equation B

substitute equation A in equation B

Solve for y

Solve the quadratic equation by graphing

The solution is y=36 cm

see the attached figure

Find the value of x

---->

therefore

Yes, it is possible  to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.

The dimensions of the cardboard sheet are 54 cm x 36 cm

Step-by-step explanation:

Let's call the width of the cardboard sheet, is the length of it (the problem states that the length is 1.5 times the width).

Also, which is the removed part of the box.

Remember that the volume of a rectangular prism is the product between each dimension. In this case, we have

Where we already included the removed part of the box.

Replacing values, we have

Using a calculator, we have

Where only the positive number make sense to the problem, because there's no negative lengths.

So, the length is

Therefore, the dimensions are 54 cm length and 36 cm width.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

step-by-step explanation: