Question

AN SOMEONE PLEASE HELP ME SOLVE THIS!!

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.

Answer 1

A) Scale factor:

Divide 2 congruent sides:

24 / 36 = 0.667

From PQR to XYZ is a 0.667 (2/3 as a fraction) scale factor.

B) Volume = (1/2 x base x side) x height:

Volume = 1/2 * 36 x 48 = 864 * 15 = 12,960 cubic inches.

C) Find the height of the prism:

7776 = (1/2 * base * sides) x height

7776 = (1/2 x 36 x 48) * height

7776 = 864 * height

Height = 7776 / 864 = 9 inches.

The scale factor is 2/3, the height of XYZ = 2/3 *9 = 6 inches.

Volume of XYZ = 1/2 x 24 x 32 = 384 x 6 = 2,304 cubic inches.