Can someone me solve
an architect is planning to make two triangular prisms out of iron. the architect will use ∆pqr for the bases of one prism and ∆xyz for the bases of the other prism.

(a)what is the scale factor from ∆pqr to ∆xyz?

(b) suppose the height of the prism made by ∆pqr is 15 inches. what is the volume of the prism made by ∆pqr? remember to show your work.

(c) suppose the volume of the prism made by ∆pqr is 7776 〖"in" 〗^3. what is the volume of the prism made by ∆xyz? remember to show your work.

Part A) The scale factor is  

Part B)The volume of the prism made by ∆PQR is

Part C) The volume of the prism made by ∆XYZ is

Step-by-step explanation:

we know that

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

In this problem triangles PQR and XYZ are similar

because

Part A) What is the scale factor from ∆PQR to ∆XYZ?

The scale factor is equal to

The scale factor is less than 1

therefore

Is a reduction

Part B) Suppose the height of the prism made by ∆PQR is 15 inches. What is the volume of the prism made by ∆PQR?

we know that

The volume of the triangular prism is equal to

where

B is the area of the base of the prism ( area of triangle ∆PQR)

h is the height of the prism

Find the area of the base B

substitute the values

Part C) Suppose the volume of the prism made by ∆PQR is 7776 〖"in" 〗^3. What is the volume of the prism made by ∆XYZ?

step 1

Find the height of the prism made by ∆PQR

The volume of the triangular prism is equal to

solve for h

we have

substitute in the formula

step 2

Find the volume of the prism made by ∆XYZ

The volume of the triangular prism is equal to

Find the area of the base B ∆XYZ

-------> see step 1

substitute the values

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step-by-step explanation:

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