Answer:
29
Step-by-step explanation:
So DF = 42, And we know that DF = DE + EF
Therefore (7x+1) + (4x-3) = 42
11x -2 = 42
11x = 44
x = 4
Substitute x = 4 onto DE equation, so 7(4) +1
= 29.
Answer: The required length of DE is 29.
Step-by-step explanation: We are given that DF = 42 in the figure shown.
We are to find the length of DE.
From the figure, we note that
[tex]DE=7x+1,~~EF=4x-3.[/tex]
According to the given information, we have
[tex]DF=42\\\\\Rightarrow DE+EF=42\\\\\Rightarrow 7x+1+4x-3=42\\\\\Rightarrow 11x=42+2\\\\\Rightarrow 11x=44\\\\\Rightarrow x=\dfrac{44}{11}\\\\\Rightarrow x=4.[/tex]
Therefore, we get
[tex]DE=7x+1=7\times4+1=28+1=29.[/tex]
Thus, the required length of DE is 29.
