The perimeter of the rectangle is 150 dm. Its length is 150 cm greater than its width. Calculate the lengths

| August 22, 2021 | education

The perimeter of the rectangle is 150 dm. Its length is 150 cm greater than its width. Calculate the lengths of the sides of the rectangle.

Let us denote by a the length of this rectangle, by b – the width of this rectangle. According to the condition of the problem, the length of the rectangle is 150 cm greater than the width, which means that the following ratio should be fulfilled:
a = b + 150
In addition, the perimeter of this rectangle is 150 dm or 1500 cm. Based on this, we can write the following ratio
2 * a + 2 * b = 1500
We solve the resulting system of equations
Substituting the value a = b + 150 from the first equation into the second equation of the system, we obtain
2 * (b + 150) + 2 * b = 1500
We solve this equation
2 * b + 2 * 150 + 2 * b = 1500
4 * b = 1500 – 2 * 150
4 * b = 1500 – 300
4 * b = 1200
b = 1200/4
b = 300
Now we find a
a = b + 150 = 300 + 150 = 450

Answer: the lengths of the sides of the rectangle are 450 cm and 300 cm



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