the length of a rectangle is twice its width w. A second triangle, which is 8cm longer and 3 cm narrower than the first triangle, has a perimeter 154 cm.

What is the dimension of each triangle.

To solve this problem, we can follow these steps:

1. Define the variables:
Let's assume that the width of the first rectangle is "w" cm. The length of the rectangle is given as twice its width, so the length of the first rectangle is "2w" cm.

2. Find the perimeter of the second triangle:
The perimeter of a triangle is the sum of its three sides. Given that the perimeter of the second triangle is 154 cm, we can form an equation:
Perimeter of the second triangle = a + b + c = 154 cm
Here, "a," "b," and "c" represent the three sides of the second triangle.

3. Express the dimensions of the second triangle in terms of the first rectangle:
We are given that the second triangle is 8 cm longer and 3 cm narrower than the first triangle. So, the dimensions of the second triangle can be expressed as:
Side "a" = 2w + 8 cm
Side "b" = w - 3 cm
Side "c" = w cm

4. Substitute the values into the equation:
Plugging in the values, we get:
(2w + 8) + (w - 3) + w = 154
Simplifying the equation gives: 4w + 5 = 154
Subtracting 5 from both sides: 4w = 149
Dividing both sides by 4: w = 37.25 cm

5. Find the dimensions of each triangle:
Using the value of "w" found in the previous step, we can calculate the dimensions of each triangle:
Length of the first triangle = 2w = 2 * 37.25 = 74.5 cm
Width of the first triangle = w = 37.25 cm

Length of the second triangle = 2w + 8 = 2 * 37.25 + 8 = 82.5 cm
Width of the second triangle = w - 3 = 37.25 - 3 = 34.25 cm

Therefore, the dimensions of the first triangle are 74.5 cm (length) and 37.25 cm (width), while the dimensions of the second triangle are 82.5 cm (length) and 34.25 cm (width).