This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the sum of the ratio parts. The ratio of the sides of the triangle is 2:3:4. The sum of the ratio parts is: 2 + 3 + 4 = 9 Step 2: Determine the length of each side. Let the common multiplier for the ratio be x. The perimeter of the triangle is 120 mm. The sum of the sides is equal to the perimeter: 2x + 3x + 4x = 120 mm 9x = 120 mm x = (120)/(9) mm = (40)/(3) mm Now, calculate the length of each side: Side 1: 2x = 2 × (40)/(3) mm = (80)/(3) mm ≈ 26.67 mm Side 2: 3x = 3 × (40)/(3) mm = 40 mm Side 3: 4x = 4 × (40)/(3) mm = (160)/(3) mm ≈ 53.33 mm Step 3: Construct the triangle using the calculated side lengths. To construct the triangle with sides (80)/(3) mm, 40 mm, and (160)/(3) mm: 1. Draw a line segment, say AB, with a length of 40 mm. This will be the base of your triangle. 2. Place the compass point at A and open it to a radius of (80)/(3) mm (approximately 26.67 mm). Draw an arc above the line segment AB. 3. Place the compass point at B and open it to a radius of (160)/(3) mm (approximately 53.33 mm). Draw another arc above the line segment AB, intersecting the first arc. 4. Label the point where the two arcs intersect as C. 5. Draw line segments AC and BC. Triangle ABC is the required triangle. The lengths of the sides of the triangle are Side 1 = (80)/(3) mm, Side 2 = 40 mm, Side 3 = (160)/(3) mm. Send me the next one 📸