Question

the perimeter of the scalene triangle is 54.6 cm. which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8 + b = 54.6

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a triangle is the sum of its three sides. For this scalene triangle, the sides are \( a \), \( 3a \), and \( b \). So, \( P = a + 3a + b \).

Step2: Substitute \( a = 8.7 \)

First, calculate \( a + 3a \) when \( a = 8.7 \). \( a + 3a = 4a \). Substitute \( a = 8.7 \): \( 4\times8.7 = 34.8 \)? Wait, no, wait. Wait, \( a + 3a = 4a \)? Wait, no, the sides are \( a \), \( 3a \), and \( b \). Wait, no, the problem: the sides are \( a \), \( 3a \), and \( b \). So perimeter is \( a + 3a + b \). Wait, but let's check again. Wait, the options: let's recalculate. Wait, \( a = 8.7 \), so \( 3a = 3\times8.7 = 26.1 \). Then \( a + 3a = 8.7 + 26.1 = 34.8 \)? Wait, no, 8.7 + 26.1 is 34.8? Wait, 8 + 26 is 34, 0.7 + 0.1 is 0.8, so 34.8. Wait, but the options: let's see the options. Wait, the first option is 8.7 + b = 54.6, second 17.4 + b, third 26.1 + b, fourth 34.8 + b. Wait, maybe I made a mistake. Wait, the sides: the triangle has sides \( a \), \( 3a \), and \( b \). So perimeter is \( a + 3a + b = 4a + b \). Wait, but when \( a = 8.7 \), \( 4a = 4\times8.7 = 34.8 \). So the equation is \( 34.8 + b = 54.6 \)? Wait, but let's check the options. Wait, the fourth option is \( 34.8 + b = 54.6 \). Wait, but let's re-express. Wait, maybe the sides are \( a \), \( 3a \), and \( b \), so perimeter is \( a + 3a + b = 4a + b \). So substituting \( a = 8.7 \), \( 4a = 34.8 \), so equation is \( 34.8 + b = 54.6 \). Wait, but let's check the options again. Wait, the options are:

1. \( 8.7 + b = 54.6 \)

1. \( 17.4 + b = 54.6 \)

1. \( 26.1 + b = 54.6 \)

1. \( 34.8 + b = 54.6 \)

Wait, maybe I misread the sides. Wait, the triangle: the base is \( 3a \), one side is \( a \), the other is \( b \). So perimeter is \( a + 3a + b = 4a + b \). So \( 4a = 4\times8.7 = 34.8 \), so equation is \( 34.8 + b = 54.6 \), which is the fourth option. Wait, but let's check again. Wait, maybe the sides are \( a \), \( 3a \), and \( b \), so \( a + 3a + b = 54.6 \). So \( 4a + b = 54.6 \). Substitute \( a = 8.7 \): \( 4\times8.7 = 34.8 \), so \( 34.8 + b = 54.6 \). So the correct equation is \( 34.8 + b = 54.6 \), which is the fourth option.

Answer:

\( 34.8 + b = 54.6 \) (the fourth option, i.e., \( 34.8 + b = 54.6 \))