[tex]\bf \triangle ABD\sim \triangle DEC\implies \cfrac{AB}{ED}=\cfrac{AC}{CD}\implies \cfrac{42}{x}=\cfrac{6}{32-x}\implies 42(32-x)=6x \\\\\\ 1344-42x=6x\implies 1344=48x\implies \cfrac{1344}{48}=x\implies 28=x[/tex]
The value of x is 28.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
According to the question
As given ΔABC ≈ ΔDEC
Therefore,
[tex]\frac{AB}{DE} = \frac{BC}{EC} = \frac{AC}{DC}[/tex] (corresponding sides have similar ratio)
Now,
[tex]\frac{AB}{DE} = \frac{AC}{DC}[/tex]
[tex]\frac{42}{6} = \frac{x}{32-x}[/tex]
[tex]7 = \frac{x}{32-x}[/tex]
224 - 7x = x
224 = 8x
x = 28
Hence, The value of x is 28.
To know more about similarity of triangle here:
https://brainly.com/question/25882965
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