Value of x is equals to 35 as per the property of the corresponding sides of two similar triangles.
What are similar triangles?
"Similar triangles are defined as the triangles with same shape but different size of side length."
Theorem used
Corresponding sides of two similar triangles are in proportion.
According to the question,
'ΔABC' represents the triangle with side lengths
4, 6, and 10 as
AB = 4
BC = 6
CA = 10
'ΔPQR' represents the triangle with side lengths
14, 21, and x as
PQ = 14
QR= 21
RP =x
Apply theorem for the given corresponding sides of a triangle we get,
[tex]\frac{AB}{PQ} =\frac{BC}{QR} =\frac{CA}{RP}[/tex]
Substitute the value in the proportion we get,
[tex]\frac{4}{14} =\frac{6}{21} =\frac{10}{x}[/tex]
⇒ [tex]\frac{2}{7} =\frac{10}{x}[/tex]
⇒[tex]x= \frac{70}{2}[/tex]
⇒[tex]x=35[/tex]
Hence, value of x is equals to 35 as per the property of the corresponding sides of two similar triangles.
Learn more about similar triangles here
https://brainly.com/question/25882965
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