A rectangle's length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm, the perimeter of the resulting rectangle will be 74 cm. Find the length and the width of the original rectangle.

Let the width of the rectangle be w cm

Length of the rectangle is 5 cm less than twice its width.

l = 2w - 5 cm

New width = old width + 2

= w + 2 cm

New length = old length - 5

= (2w - 5) - 5 cm

= 2w - 5 - 5 cm

= 2w - 10 cm

New perimeter = 2(new length + new width)

⇒ 2((2w - 10) + (w + 2)) = 74 cm

⇒ 2(2w - 10 + w + 2) = 74 cm

⇒ 2(3w - 8) = 74 cm

⇒ 6w - 16 = 74 cm

⇒ 6w = 74 + 16 cm

⇒ 6w = 90 cm

⇒ w = $\dfrac{90}{6}$ cm

⇒ w = 15 cm

Length = 2w - 5 cm

= 2 x 15 - 5 cm

= 30 - 5 cm

= 25 cm

Hence, the length is 25 cm and breadth is 15 cm.