The length of a base of a rectangular prism is twice the width of the base. the height of the prism is 3 times the width of a base. the surface area is 792 square centimeters. what are the dimensions of the prism?

The dimensions of the rectangular prism is

6cm by 12cm by 18cm [width, length and height] respectively

Step-by-step explanation:

In this question, we are asked to calculate the dimensions of a right prism given the information in the question.

Mathematically, for a right prism, the surface area is as follows;

A = 2(wl + lh + hw)

Where l, h and w represent the length, height and width respectively.

Now let’s pull the information from the question to get the dimensions.

Length is twice the width, that means l = 2w

Height is 3 times the width, that means h = 3w

Now let’s plug these two into the surface area equation, it becomes;

A = 2(2w(w) + 2w(3w) + w(3w))

A = 2(2w^2 + 6w^2 + 3w^2)

A = 2(11w^2)

A = 22w^2

Let’s insert what the value of the area is

792 = 22w^2

w^2 = 792/22

w^2 = 36

w = sqr.root 36

w = 6cm

We ignore the -6 square root answer as length cannot be negative

l = 2w = 2(6) = 12cm

w = 3w = 3(6) = 18cm

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.