The aspect ratio of the sides of the rectangle is 7:11. Find its area if the large side is 12 cm larger than the smaller one.

| January 15, 2021 | education

If the lengths of the sides of the rectangle are 7: 11, then this means that one side contains 7 parts, and the second side contains 11 of the same parts.
1) Find the lengths of the sides of the rectangle.
Let the length of one part be x cm, then one side is 7x cm, and the second side is 11x cm.By the condition of the problem, it is known that the larger side is larger than the smaller one by (11x – 7x) cm or 12 cm.Let’s make an equation and solve it.
11x – 7x = 12;
4x = 12;
x = 12: 4;
x = 3 (cm) – the length of one part;
7x = 7 * 3 = 21 (cm) – the length of one side;
11x = 11 * 3 = 33 (cm) – the length of the second side.
2) Find the area of ​​the rectangle.
The area of ​​a rectangle is equal to the product of its sides. S = ab.
S = 21 * 33 = 693 (cm ^ 2).
Answer. 693 cm ^ 2.



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