FROM THE RATIO OF SIDES AND PERIMETER FIND THE LENGTH OF EACH SIDE

Problem 1 :

The ratio of the measures of three sides of a triangle is 8:7:5. Its perimeter is 240 feet. Find the measure of each side.

Solution :

Let the three sides be 8x, 7x and 5x

Perimeter of the triangle = 240 feet

8x + 7x + 5x = 240

20x = 240

x = 240/20

x = 12

8x = 8(12) ==> 96 feet

7x = 7(12) ==> 84 feet

5x = 5(12) ==> 60 feet

So, the three sides will have measures 96 feet, 84 feet and 60 feet.

Problem 2 :

The ratio of the measures of the sides of a triangle is 3 : 4 : 5. Its perimeter is 72 inches. Find the measure of each side.

Solution :

Let the three sides be 3x, 4x and 5x

Perimeter of the triangle = 72 inches

3x + 4x + 5x = 72

12x = 72

x = 72/12

x = 6

3x = 3(6) ==> 18 inches

4x = 4(6) ==> 24 inches

5x = 5(6) ==> 30 inches

So, the three sides will have measures 18 inches, 24 inches and 30 inches.

Problem 3 :

The ratio of the measures of three sides of a triangle are 1/2 : 1/3 : 1/5, and its perimeter is 6.2 centimeters. Find the measure of each side of the triangle.

Solution :

The three sides are x/2, x/3 and x/5.

Problem 4 :

In a triangle, the ratio of the measures of three sides is 4 : 6 : 9 and its perimeter is 190 inches. Find the length of the longest side of the triangle. 

Solution :

Let the three sides be 4x, 6x and 9x

Perimeter = 190 inches

4x + 6x + 9x = 190

19x = 190

x = 190/19

x = 10

4x => 40 inches, 6x => 60 inches, 9x => 90 inches.

So, the sides are 40 inches, 60 inches and 90 inches.

Problem 5 :

The ratio of the measures of three sides of a triangle is 9 : 8 : 7, and its perimeter is 144 units. Find the measure of each side of the triangle.

Solution :

Let the three sides of the triangle are 9x, 8x and 7x.

Perimeter of triangle = 144

9x + 8x + 7x = 144

24x = 144

x = 144/24

x = 6

9x => 54, 8x => 48, 7x => 42

So, sides of the triangle are 54 units, 48 units and 42 units.