Find the area of the rectangle if the perimeter of the rectangle is 56 cm, and one side is 3 times smaller than the other.
January 19, 2021 | education
| 1) Let’s introduce a variable.
x cm – the length of the smaller side of the rectangle;
3x cm – the length of the larger side of the rectangle.
2) Let’s make an equation.
The perimeter of a rectangle is equal to the sum of the lengths of its four sides. P = 2 (a + b).
For our case, the perimeter of the rectangle is 2 (x + 3x) cm or 56 cm.We get the equation 2 (x + 3x) = 56.
3) Having solved the equation, we find the sides of the rectangle.
2 * 4x = 56;
8x = 56;
x = 56: 8;
x = 7 (cm) – the length of the smaller side;
3x = 7 * 3 = 21 (cm) – the length of the longer side.
4) Find the area of the rectangle.
The area of a rectangle is equal to the product of its sides. S = av.
7 * 21 = 147 (cm²).
Answer. 147 cm².
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