Question

PLEASE ANSWER QUICKLY

Triangles IJK and LMN are similar. Find y using proportions. Explain and show

all your steps.

Answer 1

The value of y is 45.

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,

`(Length\ of\ JK)/(Length\ of\ MN) =(Length\ of\ IJ)/(Length\ of\ ML) =(Length\ of\ IK )/(Length\ of\ LN )`

`\therefore (54)/(42) =(x)/(28) =(y)/(35)`

`(54)/(42) =(y)/(35)`

By using cross multiplication method, we get;

`42y=54*35\\\\y=(54*35)/(42)=9*5=45`

Similarly we can find the value of x;

`(54)/(42) =(x)/(28)`

By using cross multiplication method, we get;

`42x=54*28\\\\x=(54*28)/(42) =9*4=36`

Thus the value of y is 45.