# The pattern of a piece of clothing has the shape of an isosceles right-angled triangle, the leg length of which is 4 dm.

**The pattern of a piece of clothing has the shape of an isosceles right-angled triangle, the leg length of which is 4 dm. How many of these parts can be cut from a piece of rectangular fabric measuring 4m by 2m 40cm?**

Let’s immediately translate decimeters into meters:

4 dm = 0.4 m.

Find the area of the part pattern. Since it has the shape of a right-angled triangle, we will look for it using the following formula:

Sv = 1 / 2ab, where a and b are the legs of the triangle.

Let’s calculate the area:

Sw = ½ * 0.4 * 0.4 = 0.08 dm².

Now we will find the area of a piece of fabric. It has a rectangular shape, so we will search by the formula:

Stk = cd, where c and d are the length and width of the fabric.

Let’s calculate the area of the fabric:

Stk = 4 * 2.4 = 9.6 m².

To answer the question of the problem, we find how many times the area of a piece of fabric is greater than the area of the pattern of the part:

9.6 / 0.08 = 120.

Answer: 120 patterns of a part can be cut from a piece of rectangular fabric.