A rectangular piece of cardboard has a length of 32 cm. Squares of 4cm on a side are cut out of each corner of the rectangle so that the remaining piece can be folded into an open-topped box. IF the volume of the box is 768 cubic cm, what is the area of the original piece of cardboard?

518 cm²

Step-by-step explanation:

We are told the length is 32 cm from the question.

Now, if 4 cm squares are removed from the width sides, it means it will now be lesser by 4 + 4 = 8 cm.

This means that the height will be 4 cm.

If length is L and width is W.

This means if 4 cm is cut from both sides, length is now;

L - 8 = 32 - 8 = 24 and width is w - 8

Volume of a cube is;

V = Lwh

Thus, we have;

V = 24 × (w - 8) × 4

We are told the volume is 786 m³

Thus;

24 × (w - 8) × 4 = 786

96(w - 8) = 786

w - 8 = 786/96

w - 8 = 8.1875

w = 8 + 8.1875

w = 16.1875

Thus,area = lw = 32 × 16.1875 = 518 cm²

answer: check all that apply, where the options?

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it