The length of the rectangle is 7cm longer than its width. If you divide the length by 3

The length of the rectangle is 7cm longer than its width. If you divide the length by 3 and add 4cm to the width, then the perimeter will be 24 cm less than it was. Find the width.

Initial length rectangular. (a1) -? cm, 7 cm more than b1;

Initial width rectangular. (b1) -? cm;

Perimeter of origin (Ppr. 1) -? cm;

Length received. rectangular. (a2) -? cm, 3 times less than a1;

Receive width rectangular. (b2) -? cm, 4 cm more than b1;

Perimeter received (Ppr. 2) -? cm, 24 cm less than Ppr. 1.

Express the width of the original rectangle in terms of its length:

b1 = a1 + 7 (cm).

Now let’s express the length and width of the resulting rectangle:

a2 = a1 / 3 (cm);

b2 = b1 + 4 (cm).

The perimeter of the rectangle is calculated using the formula:

Ppr. = (a + b) * 2.

Hence, the perimeter of the original rectangle is:

Ppr. 1 = (a1 + b1) * 2, and the resulting Ppr. 2 = (a2 + b2) * 2.

Because Ppr. 1 – Ppr. 2 = 24 cm, then (a1 + b1) * 2 – (a2 + b2) * 2 = 24.

Substitute the expressions obtained above into this equality:

(a1 + b1) * 2 – (a2 + b2) * 2 = 24;

(a1 + a1 + 7) * 2 – (a1 / 3 + b1 + 4) * 2 = 24;

(2a1 + 7) * 2 – (a1 / 3 + b1 + 4) * 2 = 24;

(2a1 + 7) * 2 – (a1 / 3 + (a1 + 7) + 4) * 2 = 24;

(2a1) * 2 – (a1 / 3 + a1 + 11) * 2 = 24;

4a1 + 14 – (2a1 / 3 + 2a1 + 22) = 24;

4a1 + 14 – 2a1 / 3 – 2a1 – 22 = 24;

2a1 – 8 – 2a1 / 3 = 24;

2a1 – 2a1 / 3 = 32;

(6a1 – 2a1) / 3 = 32;

6a1 – 2a1 = 96;

4a1 = 96;

a1 = 24 (cm) – the length of the original rectangle.

Then the width of the original rectangle is:

b1 = a1 + 7 = 24 + 7 = 31 (cm).

Answer: The width of the original rectangle is 31 cm.