Verified answer

For the first triangle, let x be the length. Then the width is x-5 (5 meters less than the length). The area is 1/2 base times height, or 1/2*x*(x-5).

In the second triangle, the length is shortened by 2m, so it's x-2. The width is increased by 1m, which is (x-5)+1 or (x-4). The area of the second triangle is 1/2(x-2)(x-4).

Find x when the two areas are the same:

1/2*x*(x-5)=1/2(x-2)(x-4)

First, multiply both sides by 2 to get rid of those pesky fractions

x(x-5)=(x-2)(x-4)

Multiply out both sides:

x²-5x=x²-4x-2x+8

Combine like terms:

x²-5x=x²-6x+8

Subtract x² from both sides:

-5x=-6x+8

Add 6x to both sides:

x=8

The length is 8m and the width is 3m.