Answer :
To solve the problem, follow these steps:
1. Understand the Ratios: The sides of the triangle are in the ratio of 21:8:14. This means if the smallest side is given a size of '8x', the second side is '21x', and the third side is '14x'. The ratio helps us express each side in terms of a single unknown, 'x'.
2. Set Up the Equation Using the Perimeter: The perimeter of the triangle is given as 215 feet. This means if you add all the sides of the triangle together, the sum will be 215 feet.
Therefore, the equation is:
[tex]\( 21x + 8x + 14x = 215 \)[/tex]
3. Combine Like Terms: Combine the terms on the left side to simplify the equation:
[tex]\( (21 + 8 + 14)x = 215 \)[/tex]
[tex]\( 43x = 215 \)[/tex]
4. Solve for [tex]\( x \)[/tex]: To find the value of [tex]\( x \)[/tex], divide both sides by 43:
[tex]\( x = \frac{215}{43} \)[/tex]
[tex]\( x = 5 \)[/tex]
5. Calculate the Length of Each Side: Now, use the value of [tex]\( x \)[/tex] to find the length of each side.
- For the first side (21x):
[tex]\( 21 \times 5 = 105 \)[/tex] feet
- For the second side (8x):
[tex]\( 8 \times 5 = 40 \)[/tex] feet
- For the third side (14x):
[tex]\( 14 \times 5 = 70 \)[/tex] feet
6. Conclusion: The lengths of the sides of the triangle are 105 feet, 40 feet, and 70 feet.
These steps give you the side lengths of the triangle while maintaining the given perimeter and the specified ratio.
1. Understand the Ratios: The sides of the triangle are in the ratio of 21:8:14. This means if the smallest side is given a size of '8x', the second side is '21x', and the third side is '14x'. The ratio helps us express each side in terms of a single unknown, 'x'.
2. Set Up the Equation Using the Perimeter: The perimeter of the triangle is given as 215 feet. This means if you add all the sides of the triangle together, the sum will be 215 feet.
Therefore, the equation is:
[tex]\( 21x + 8x + 14x = 215 \)[/tex]
3. Combine Like Terms: Combine the terms on the left side to simplify the equation:
[tex]\( (21 + 8 + 14)x = 215 \)[/tex]
[tex]\( 43x = 215 \)[/tex]
4. Solve for [tex]\( x \)[/tex]: To find the value of [tex]\( x \)[/tex], divide both sides by 43:
[tex]\( x = \frac{215}{43} \)[/tex]
[tex]\( x = 5 \)[/tex]
5. Calculate the Length of Each Side: Now, use the value of [tex]\( x \)[/tex] to find the length of each side.
- For the first side (21x):
[tex]\( 21 \times 5 = 105 \)[/tex] feet
- For the second side (8x):
[tex]\( 8 \times 5 = 40 \)[/tex] feet
- For the third side (14x):
[tex]\( 14 \times 5 = 70 \)[/tex] feet
6. Conclusion: The lengths of the sides of the triangle are 105 feet, 40 feet, and 70 feet.
These steps give you the side lengths of the triangle while maintaining the given perimeter and the specified ratio.
