Question

Sissy wants to enlarge a picture of a constellation so that she can put it on the wall in her daughter’s room. What will be the area of the enlarged picture on the wall?
24 in.2
108 in.2
224 in.2
486 in.2

Answer 1

Answer: 486 in

Just did this on edge

Answer 2

The enlargement transformation applied to the rectangular figure gives

a rectangle that is enlarged and similar to the figure.

Correct response:

• The area of the enlarged picture is 486 in.²

The given dimensions of the picture are;

Height, $\overline{MN}$ = 6 in.

Width, $\overline{LP}$ = 4 in.

The length of QL' = 12  + 42 = 54

By similar triangles, we have;

$\dfrac{\overline{L'P'}}{\overline{LP}} = \mathbf{ \dfrac{\overline{QL'}}{\overline{QL}}}$

Which gives;

$\dfrac{\overline{L'P'}}{6} = \mathbf{ \dfrac{54}{12}}$

$\overline{L'P'} = \dfrac{54 }{12} \times 6 = \mathbf{27}$

Given that an enlargement gives similar figures, we have;

$\dfrac{\overline{L'P'}}{\overline{LP}} = \mathbf{\dfrac{\overline{L'M'}}{\overline{LM}}} = Scale \, factor \ of \ the \ enlargement$

Therefore;

$\dfrac{27}{6} = \dfrac{\overline{L'M'}}{4}$

Which gives;

$\overline{L'M'} = \dfrac{27}{6} \times 4 = \mathbf{ 18}$

The area of the enlarged picture is, A = $\overline{L'M'}$ × $\overline{L'P'}$

Which gives;

A = 27 × 18 = 486

• The area of the enlarged picture on the wall is A = 486 in.²

Learn more about scale factors and enlargement transformation here:

https://brainly.com/question/14215765

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