The sides of one quadrangle are related as 3: 5: 7: 11, and the total length of the longest and smallest sides

| February 23, 2021 | education

The sides of one quadrangle are related as 3: 5: 7: 11, and the total length of the longest and smallest sides of another quadrilateral, similar to the first one, is 56 dm. Find the sides of the other quadrangle.

If the quadrangles are similar, then their respective sides are proportional. This means that the sides of the second quadrangle are the same as the sides of the first 3: 5: 7: 11. The larger side is proportional to 11, and the smaller is 3. Let’s take one part for x, then the length of the smaller side will be 3x, and the length of the larger side will be 11x. It is known that the sum of the lengths of the smaller and larger sides is equal to (3x + 11x) dm or 56 dm. Let’s make an equation and solve it.

3x + 11x = 56;

14x = 56;

x = 56: 14;

x = 4 (cm) – length of one part;

3x 4 * 3 = 12 (dm) – the length of the smaller side;

11x = 4 * 11 = 44 (dm) – the length of the longer side;

The lengths of the other two sides will be 5x and 7x. Let’s find them.

5x = 4 * 5 = 20 (dm);

7x = 4 * 7 = 28 (dm).

Answer. 12 dm, 20 dm, 28 dm, 44 dm.



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