Question

quiz 1: ratios and proportions
the lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5. the perimeter of the triangle is 32 feet. the length of the longest side is
4 feet
20 feet
28 feet
none of these choices are correct

Explanation:

Step1: Define variables for sides

Let the sides of the triangle be \( x \), \( 2x \), and \( 5x \) (since the ratio is \( 1:2:5 \)).

Step2: Set up perimeter equation

The perimeter of a triangle is the sum of its sides. So, \( x + 2x + 5x = 32 \).

Step3: Solve for \( x \)

Combine like terms: \( 8x = 32 \). Divide both sides by 8: \( x = \frac{32}{8} = 4 \).

Step4: Find the longest side

The longest side is \( 5x \). Substitute \( x = 4 \): \( 5(4) = 20 \) feet.

Answer:

20 feet (corresponding to the option with "20 feet")