Question

These two figures are the image and pre-image of a dilation. Find the length of the missing sides.

Answer 1

Answer:

Hence, we have:

           x= 5/2 in.=2.5 in.

and y+1=6 in.    ( since y=5)

Step-by-step explanation:

We know that if two triangles are similar then there corresponding sides are proportional.

i.e. according to  the figure provided to us we have:

$\dfrac{4}{2}=\dfrac{5}{x}=\dfrac{y+1}{3}$

On equating the first two equality we have:

$\dfrac{4}{2}=\dfrac{5}{x}\\\\i.e.\\\\4x=10\\\\x=\dfrac{10}{4}\\\\\\x=\dfrac{5}{2}$

    Hence,   x=5/2 in.

and now on equating first and third terms we have:

$\dfrac{4}{2}=\dfrac{y+1}{3}\\\\12=2(y+1)\\\\12=2y+2\\\\12-2=2y\\\\i.e.\\\\2y=10\\\\i.e.\\\\y=5$

Hence, the length of the missing sides are:  

x=5/2 in.

and y+1=5+1=6 in.

Answer 2

The measure of x and y is 2.5 and 4

The two triangles shown here are similar triangles

Using the similarities theorem of the triangle;

4/2 = 5/x

Cross multiply

4x = 2 * 5

4x = 10

x = 10/4

x = 2.5

Similarly;

4/2 = y+1/2.5

2.5 * 4 = 2(y+1)

10 = 2(y+1)

5 = y+ 1

y = 5 - 1

y = 4

Hence the measure of x and y is 2.5 and 4

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