You solve this with help of H.C.F =76cm,152cm,114
the maximum size scale is 38cm(ans)

Maximum Size Scale to Measure 3 Equilateral Triangles

To measure the three equilateral triangles with sides measuring 114 cm, 76 cm, and 152 cm exactly, we need to find the maximum size scale that can be used. Let's break down the process step by step:

Step 1: Understanding Equilateral Triangles
An equilateral triangle is a type of triangle where all three sides are equal in length, and all three angles are 60 degrees. This makes it a special type of regular polygon.

Step 2: Using Similar Triangles
To find the maximum size scale that can measure the given triangles exactly, we can use the concept of similar triangles. Similar triangles have the same shape but may differ in size.

Step 3: Determining the Scale Factor
The scale factor between two similar triangles is the ratio of their corresponding sides. In this case, we need to find the scale factor between the given equilateral triangles and the measuring scale.

Let's calculate the scale factor for each triangle:

- Triangle 1: Side length = 114 cm
- Triangle 2: Side length = 76 cm
- Triangle 3: Side length = 152 cm

To measure these triangles, we need to find a scale factor such that when we multiply the side lengths of the triangle with the scale factor, the resulting values are integers.

Step 4: Finding the Common Scale Factor
To find the common scale factor, we need to find the greatest common divisor (GCD) of the side lengths of the triangles. The GCD will be the scale factor that can be used to measure all three triangles exactly.

Calculating the GCD of the side lengths:

- GCD(114, 76) = 38
- GCD(38, 152) = 38

The GCD of the three side lengths is 38 cm. Therefore, the maximum size scale that can measure the three triangles exactly is 38 cm.

Step 5: Measuring the Triangles
Using the 38 cm scale, we can measure each side of the triangles by dividing the side length by the scale factor:

- Triangle 1: 114 cm / 38 cm = 3 units
- Triangle 2: 76 cm / 38 cm = 2 units
- Triangle 3: 152 cm / 38 cm = 4 units

Using the 38 cm scale, we can measure all three equilateral triangles exactly.

Conclusion
To measure the equilateral triangles with side lengths of 114 cm, 76 cm, and 152 cm exactly, we found that the maximum size scale that can be used is 38 cm. By dividing the side lengths of the triangles by the scale factor, we obtain the measurements in units using the 38 cm scale. This ensures accurate and precise measurements of the equilateral triangles.