Question

A triangle has side lengths of 4 inches, 5 inches, y 1 inches. Another triangle has side lengths of 2 inches, x inches, 3 inches. These two figures are the image and pre–image of a dilation. Find x and y. X = y =.

Answer 1

Similar triangles sides are in ratio. The value of x and y is 2.5 and 5 respectively.

What are similar triangles?

If the respective angles are congruent and the corresponding sides are proportional, two triangles are said to be similar.

As it is given that these two figures are the image and pre-image of a dilation, therefore, the two triangles are similar triangles.

We know that when two triangles are similar triangles, then the ratio of their corresponding sides is the same. Thus,

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

Now, the value of x and y can be written as,

$\dfrac{4}{2}=\dfrac{5}{x}\\\\x = \dfrac{5 \times 2}{4}\\\\x = 2.5$

Also,

$\dfrac{4}{2}=\dfrac{y+1}{3}\\\\4 \times 3 = (y+1)2\\\\12=2y+2\\\\2y = 12-2\\\\y = 5$

Hence, the value of x and y is 2.5 inches and 5 inches respectively.

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Answer 2

Answer:

x = 2.5 y = 5

Step-by-step explanation: