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

Answer:

The height of the prism is 7 unit  

Step-by-step 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 = $\dfrac{1}{2}$ ×  $b_1$ ×  $b_2$× height

Or, v =  $\dfrac{1}{2}$ ×  $b_1$ ×  $b_2$× h

Or, 21 cubic unit =  $\dfrac{1}{2}$ × 2 unit × 3 unit × h unit

Or, 21 =  $\dfrac{1}{2}$ × 6 × h

Or, 21 = 3 × h

∴   h = $\dfrac{21}{3}$

i.e h = 7 unit

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

Hence, The height of the prism is 7 unit  Answer