Answer:
The value of y is 45.
Step-by-step explanation:
Given,
ΔIJK and ΔLMN are similar.
Length of JK = 54
Length of MN = 42
Length of ML = 28
Length of LN = 35
Solution,
Since, ΔIJK and ΔLMN are similar. So the ratio of the length of their corresponding sides are equal.
This is because of similarity theorem of triangle, which states that;
"If two triangles are similar then the corresponding angles are equal and the ratio of the length of their corresponding sides are also equal."
So,
[tex]\frac{Length\ of\ JK}{Length\ of\ MN} =\frac{Length\ of\ IJ}{Length\ of\ ML} =\frac{Length\ of\ IK }{Length\ of\ LN }[/tex]
[tex]\therefore \frac{54}{42} =\frac{x}{28} =\frac{y}{35}[/tex]
[tex]\frac{54}{42} =\frac{y}{35}[/tex]
By using cross multiplication method, we get;
[tex]42y=54\times35\\\\y=\frac{54\times35}{42}=9\times5=45[/tex]
Similarly we can find the value of x;
[tex] \frac{54}{42} =\frac{x}{28} [/tex]
By using cross multiplication method, we get;
[tex]42x=54\times28\\\\x=\frac{54\times28}{42} =9\times4=36[/tex]
Thus the value of y is 45.
