The difference between the two sides of the rectangle is 7 cm, and its perimeter is 54 cm. Find the sides of the rectangle.

Let’s say Y is the length of the rectangle and X is its width.

Then:

– the difference between the sides of the rectangle can be expressed by the equation: X – Y = 7;

– the perimeter of this rectangle can be written as the following equation:

2 x (X + Y) = 54.

Let’s solve these equations.

1.

X – Y = 7; X = 7 + Y.

2.

2 x (X + Y) = 54;

X + Y = 27.

Substitute in the second equation the value of X from the first equation (X = 7 + Y):

7 + Y + Y = 27;

2U = 20;

Y = 10.

3.

Now the calculated value of Y, we substitute in the first equation to calculate the value of X:

X = 7 + Y = 7 + 10 = 17.

Answer: The length of the rectangle is 10cm and the width is 17cm.