Answer:
The height of the prism is 5 inches
Step-by-step explanation:
The rule of the lateral area of the rectangular prism is
L.A = 2(L + W) × H, where
- L is the length of the base of the prism
- W is the width of the base of the prism
- H is the height of the prism
∵ A rectangular prism has a length of 9 inches and a width of 8 inches
∴ L = 9 inches
∴ W = 8 inches
∵ The lateral area of it is 170 square inches
∴ L.A = 170 square inches
→ Substitute them in the rule above to find the height of the prism
∵ 170 = 2(9 + 8) × H
∴ 170 = 2(17) × 5
∴ 170 = 34 × H
→ Divide both sides by 34 to find H
∴ 5 = H
∴ The height of the prism is 5 inches.
