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

| August 10, 2021 | education

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

If the quadrangles are similar, then their respective sides are proportional. And the sides of the second triangle are related to each other in the same way as the sides of the first, that is, as 3: 5: 7: 11. This means that one part contains x dm, then the first side is equal to 3x dm, the second – 5x dm, the third – 7x dm and the fourth – 11x dm. It is known that the sum of the largest and smallest 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 (dm) – one part of the length;

3x = 4 * 3 = 12 (cm) – 1 side;

5x = 4 * 5 = 20 (cm) – 2 side;

7x = 4 * 7 = 28 (cm) – 3rd side;

11x = 4 * 11 = 44 (cm).

Answer. 12 cm, 20 cm, 28 cm, 44 cm.



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