The length of a rectangle is 3cm longer than its width. Its perimeter is 22cm.

| March 19, 2021 | education

The length of a rectangle is 3cm longer than its width. Its perimeter is 22cm. Find the length and width by the linear equation method with two unknowns.

Let us determine, by compiling a system of equations, what the measurements of the rectangle are equal to.

Let’s designate its length as “x”, and take its width as “y”. The perimeter is 22 cm, one side is 3 cm larger than the other.

Let’s recall the formula for calculating the sum of all sides: P = 2a + 2b.

Consequently:

2 * x + 2 * y = 22.

x = y + 3.

Substitute the second expression “x” for the first equation:

2 * (y + 3) + 2y = 22.

Let’s expand the brackets:

2y + 6 + 2y = 22.

We perform actions with the coefficients of the variable on the left side of the equation, and transfer the number to the right, while the sign in front of it changes to the opposite:

4y = 22 – 6 = 16.

To find the second factor, divide the product by the first:

y = 16: 4 = 4.

The width of the rectangle = 4 cm and its length = 4 + 3 = 7 cm.



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