Mathematics: Use the given area to find stuff a. 13.5 in. b. 15 in. c. 22.5 in. d. 25 in.

Step-by-step explanation:simplify to get...

Use the given area to find stuff a. 13.5 in. b. 15

Ответ:

xcncxgnfxg6487

16.01.2022

Mathematics

Option B. $XY=15\ in$

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z----> the scale factor

x----> area of the larger pentagon (UVWXY)

y----> area of the smaller pentagon (LMNPO)

$z^{2}=\frac{x}{y}$

we have

$x=198\ in^{2}$

$y=88\ in^{2}$

substitute

$z^{2}=\frac{198}{88}$

$z^{2}=2.25$

z=1.5

step 2

Find XY

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

x----> side XY of the larger pentagon (UVWXY)

y----> side OP of the smaller pentagon (LMNPO)

$z=\frac{x}{y}$

we have

z=1.5

$y=10\ in$

substitute

$1.5=\frac{x}{10}$

$x=1.5*10=15\ in$

therefore

$XY=15\ in$

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Use the given area to find stuff

a. 13.5 in.
b. 15 in.
c. 22.5 in.
d. 25 in.

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