Question

12) The ratio of the measures of the three sides of a triangle is 4:6:9, and its perimeter

is 190 inches. Find the measure of each side of the triangle. Show proportions.

Answer 1

To determine the measures of the triangle's sides with a side ratio of 4:6:9 and a 190-inch perimeter, establish a common multiplier x for the sides, solve for x using the perimeter, and then calculate each side's measurement.

Step-by-step explanation:

To find the measure of each side of a triangle with a ratio of the sides being 4:6:9 and a perimeter of 190 inches, we can set up proportions. Let's denote the sides as 4x, 6x, and 9x where x is the common multiplier. Since the perimeter is the sum of all sides, we have:

4x + 6x + 9x = 190

Simplifying this equation we get:

19x = 190

Dividing both sides by 19:

x = 10

Now we can find the actual lengths of the sides:

• Side 1 = 4x = 4(10) = 40 inches
• Side 2 = 6x = 6(10) = 60 inches
• Side 3 = 9x = 9(10) = 90 inches