Question

1-65b. the perimeter of the triangle at right is 52 units.

7x−4

19

10x+3

use the equation for perimeter from the last problem to solve for x.

x =

now that you know what x is, find the measure of each side. you know that one side is 19, but what are the other two?

7x − 4 =

10x + 3 =

be sure to confirm that your answer is correct. in other words, see your side lengths add up to 52.

Explanation:

Solución para \( x \)

Step1: Escribir la fórmula del perímetro

El perímetro de un triángulo es la suma de sus lados. Entonces, \( (7x - 4) + (10x + 3) + 19 = 52 \).

Step2: Simplificar la ecuación

Combinar términos semejantes: \( 7x + 10x - 4 + 3 + 19 = 52 \) → \( 17x + 18 = 52 \).

Step3: Resolver para \( x \)

Restar 18 de ambos lados: \( 17x = 52 - 18 \) → \( 17x = 34 \). Dividir por 17: \( x = \frac{34}{17} = 2 \).

Step1: Sustituir \( x = 2 \)

Sustituir \( x = 2 \) en \( 7x - 4 \): \( 7(2) - 4 \).

Step2: Calcular

\( 14 - 4 = 10 \).

Step1: Sustituir \( x = 2 \)

Sustituir \( x = 2 \) en \( 10x + 3 \): \( 10(2) + 3 \).

Step2: Calcular

\( 20 + 3 = 23 \).

Answer:

\( x = 2 \)

Medida de \( 7x - 4 \)