The bottom and top of a box are rectangles twice as long as they are wide. find the volume of the box if it is four feet high and has a total surface area of 220 feet squared.

Let x = the width

then

2x = the length

:

The box dimensions: 2x by x by 4

Given the surface area:

2(2x*x) + 2(2x*4) + 2(x*4) = 220

:

4x^2 + 16x + 8x = 220

A quadratic equation:

4x^2 + 24x - 220 = 0

simplify, divide by 4

x^2 + 6x - 55 = 0

Factor

(x+11)(x-5) = 0

The positive solution is what we want here:

x = 5 ft is the width

then

2(5) = 10 ft is the length

:

Find the volume

10 * 5 * 4 = 200 cu/ft is the volume

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