Question

The prism below has a volume of 21 cubic units.The base is a right triangle with legs that have lengths of 2 units and 3 units,Find the height of the prism

Answer 1

The base (b) of the triangle is

✔ 3

units.

The height (h) of the triangle is

✔ 5

units.

The area of the triangle is

✔ 7.5

square units.

Explanation:

Answer 2

The height of the prism is 7 unit

Explanation:

Given as :

The volume of right triangle prism = v = 21 cubic unit

The length of one base =
`b_1` = 2 unit

The length of other base =
`b_2` = 3 unit

Let The height of the prism = h unit

Now, According to question

Volume of prism =
`(1)/(2)` ×
`b_1` ×
`b_2`× height

Or, v =
`(1)/(2)` ×
`b_1` ×
`b_2`× h

Or, 21 cubic unit =
`(1)/(2)` × 2 unit × 3 unit × h unit

Or, 21 =
`(1)/(2)` × 6 × h

Or, 21 = 3 × h

∴ h =
`(21)/(3)`

i.e h = 7 unit

So,The height of the prism = h = 7 unit

Hence, The height of the prism is 7 unit Answer