Question

the right triangular prism and the square rectangular prism both haven't had a 10 in in the same volume. A plane slices both solid parallel to their bases. The base of the triangular prism is a right triangle with legs 8 and 9 in Long. Find the length of the side of the square prism's cross-section in inches.​

Answer 1

Answer:  6 inches

Step-by-step explanation:

Volume (V) = Area of the base (B) × height (h)

Both images have the same volume and the same height, therefore the Area of their bases must be equal to each other.

Area of the triangle

$A=\dfrac{1}{2}\cdot b \cdot h\\\\.\quad=\dfrac{1}{2}\cdot 8 \cdot 9\\\\.\quad= 36$

Area of a square

A = s²

36 = s²

6 = s