Question

The polygons are similar find the value of x and y.

A. X= 24 and Y= 27
B. X= 13.5 and Y= 27
C. X= 24 and Y= 48
D. X= 13.5 and Y= 48

Answer 1

Answer:

A

Step-by-step explanation:

by similarity x/40=18/30

so x= 40×18/30

x=24

also y/30=36/40

y =30×36/40

y =27

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Answer 2

Answer:

A) x = 24 and y = 27

Step-by-step explanation:

In similar polygons, corresponding sides are always in the same ratio.

Therefore, to find the values of x and y, we can set up the following ratios for the corresponding sides of the given triangles:

$\dfrac{x}{18}=\dfrac{40}{30}=\dfrac{36}{y}$

Solve for x:

$\begin{aligned}\dfrac{x}{18}&=\dfrac{40}{30}\\\\x \cdot 30&=40 \cdot 18\\\\30x&=720\\\\\dfrac{30x}{30}&=\dfrac{720}{30}\\\\x&=24\end{aligned}$

Solve for y:

$\begin{aligned}\dfrac{40}{30}&=\dfrac{36}{y}\\\\40 \cdot y&=36 \cdot 30\\\\40y&=1080\\\\\dfrac{40y}{40}&=\dfrac{1080}{40}\\\\y&=27\end{aligned}$

Therefore, the values of x and y are:

$\Large\boxed{\boxed{x = 24\;\;\textsf{and}\;\;y = 27}}$