The width of the rectangular parallelepiped is 42 cm, which is 7/15 of its length, and the height is 5/9 of its length.

The width of the rectangular parallelepiped is 42 cm, which is 7/15 of its length, and the height is 5/9 of its length. Find the volume of a parallelepiped?

1. First, let’s calculate the length. If the width is 42 cm and this is 7/15 of its length, then we can find the length by applying the method of proportions and denoting the desired length with the letter X:
7/15 – 42;
1 – H.
Where from:
X = (42 x 1) / 7/15;
X = 42 x 15/7;
X = 90 (cm).
2. Now let’s find the height. If it is equal to 5/9 of the length, then by the same method we will find it, denoting it with the letter Y:
1 – 90;
5/9 – W.
Where from:
Y = 90 x 5/9 / 1;
Y = 50 (cm).
3. Knowing the length, width and height, it is easy to calculate the volume of this parallelepiped. To do this, you need to multiply these three values:
90 x 42 x 50 = 189000 (cm³).
Answer: the volume of this parallelepiped is 189,000 cubic centimeters.