Question

the right rectangular prism shown has a length of 8ft a width of 2ft and a height of 6ft the dimensions of the prism are doubled​

Answer 1

Answer:

Part 1) The scale factor is $2$

Part 2) The dimensions of the enlarged prism are

a.Length=(8)(2)=16 ft

b.Width=(2)(2)=4 ft

c.Height=(6)(2)=12 ft

Part 3) The surface area of the smaller rectangular prism is 152 ft^{2}

Step-by-step explanation:

we now that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Part 1)

Find the scale factor

we know that

If the dimensions of the smaller prism are doubled , then the scale factor from the smaller rectangular prism to the larger rectangular prism is equal to $2$

Part 2)

we know that

To find the dimensions of the enlarged figure, multiply the dimensions of the smaller prism by the scale factor

so

Length=(8)(2)=16 ft

Width=(2)(2)=4 ft

Height=(6)(2)=12 ft

Part 3) Find the surface area of the smaller rectangular prism

we know that

The surface area of the rectangular prism is equal to the area of its six rectangular faces

SA=2(8)(2)+2(2)(6)+2(8)(6)=152 ft^{2}