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Algebra Difficulty 1.7 Junior Find the answer Canada

All three scales shown are balanced.

One possible replacement for the ? is

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The triangular prism given can be created by slicing the 3 cm by 4 cm base of a rectangular prism with equal height across its diagonal.
That is, the volume of the triangular prism in question is one half of the volume of the rectangular prism shown.

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Since the volume of the triangular prism is 120 cm $^3$ , then the volume of this rectangular prism is $2\times120=240$ cm $^3$ .

The volume of the rectangular prism equals the area of its base $3\times 4$ times its height, $h$ .

Since the volume is 240, then $3\times 4 \times h=240$ or $12h=240$ , so $h=\frac{240}{12}=20$ .
Since the height of this rectangular prism is equal to the height of the triangular prism in question, then the required height is 20 cm.

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