Answered

A segment 35 centimeters long is divided into two segments whose ratio is 3:4.How long is each segment?

Sagot :

Jeremiaid
Given:  35 cm = the measure of the segment
           3 : 4 = the ratio of the two shorter segments divided from 35 cm

Asked: How long is each segment?

Mathematical sentence: 
                   
       [tex]35 cm [/tex] x [tex] \frac{3}{3 + 4} [/tex] = length of the shorter segment
       [tex]35 cm[/tex] x [tex] \frac{4}{3 + 4} [/tex] = length of the longer segment

Solution:
       Length of the shorter segment =
                 [tex]35 cm [/tex] x [tex] \frac{3}{3 + 4} [/tex]
                 [tex]35 cm [/tex] x [tex] \frac{3}{7} [/tex]
                 [tex] \frac{105 cm}{7} [/tex]
                 15 cm
 Length of the shorter segment =  15 cm
        
        Length of the longer segment: 
                 [tex]35 cm[/tex] x [tex] \frac{4}{3 + 4} [/tex]
                 [tex]35 cm[/tex] x [tex] \frac{4}{7} [/tex]
                 [tex] \frac{140 cm}{7} [/tex]
                 20 cm
Length of the longer segment = 20 cm

Check: 15 : 20 or [tex] \frac{15}{20} [/tex] = 3 : 4 or [tex] \frac{3}{4} [/tex]
  Cross multiply:
                          15 x 4 = 20 x 3
                            60 = 60, CORRECT
 Therefore: 
               Length of the shorter segment =  15 cm
               Length of the longer segment = 20 cm
           

Elensapid
[tex]|^{\underline{~~~~~~~~~~~~~~X~~~~~~~~~~~~~~~~~}}|^{\underline{~~~~~~~~~~~~Y~~~~~~~~~~~~}}| \\ X+Y=35~cm \\ \frac{Y}{X}= \frac{3}{4} \Longrightarrow 4Y=3X \Longrightarrow X= \frac{4Y}{3} \\ \frac{4Y}{3}+^{3)}Y=^{3)}35 \\ \frac{4Y}{3}+ \frac{3Y}{3}= \frac{105}{3}|*3 \\ 7Y=105 \\ \boxed{Y=15~cm} \\ X=35-15 \\ \boxed{X=20~cm} [/tex]