In a block building game, Belén has 56 cubes of 1 unit in side length. Using all of them, she built a rectangular prism with a base perimeter of 22 unit lengths. What is the height of the prism?

Answers choices: 8,7,6,4,3,2,1

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Given:–Answers choices: 8,7,6,4,3,2,1

Answer:–we know that,

Let , height of prism is H unit .

so,

→ Volume of prism = Volume of cubes of 1 unit side length

→ (L * B) * H = 56 * (1)³

→ (L * B) * H = 56

now, given that,

→ 2(L + B) = 22

→ (L + B) = 11

taking, possible values of L and B, and if we assume that , all L , B and H are positive integers , then,

therefore, we can conclude that, values of L and B are 7 and 4 .

hence,

→ 7 * 4 * H = 56

→ H =

2 unit(Ans.)[ Note :- In question it should be mentioned that H must a integer . otherwise we have to check options. ]

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Given :In a block building game, Belén has 56 cubes of 1 unit in side length. Using all of them, she built a rectangular prism with a base perimeter of 22 unit lengths.To Find :height of the prism8,7,6,4,3,2,1

Solution:a base perimeter of 22 unit lengths.

Which can be

Base perimeter = 2 ( l + b)

2 (1 + 10)

2 ( 2 + 9)

2 ( 3 + 8)

2 ( 4 + 7)

2 ( 5 + 6)

now l * b * h = 56

only possible when

4 * 7 * 2 = 56

Hence base area 4 * 7

and height is 2

height of the prism is 2 unit

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