Mathematics: The area of a mirror is 225 square inches, it s width is [tex]13 rac{3}{4} [/tex]inches. will the mirror fit in a space that is 15 inches by 16 inches? explain.

The area of a mirror is 225 square inches, it s

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14.01.2022

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Solution:

Given that area of mirror is 225 square inches

$width = 13\frac{3}{4} \text{ inches }$

Converting the above mixed fraction we get,

$width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }$

Let us find the length of mirror

The area of mirror is given as:

area of mirror = length x width

Substituting the given values,

$225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36$

Thus length of mirror is 16.36 inches

Will the mirror fit in a space that is 15 inches by 16 inches?

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Because length of mirror is 16.36 inches whereas the given space is 15 inches long

16.36 > 15 so the length of mirror will not fit inside the space

Also width of mirror is $\frac{55}{4} = 13.75$ inches which is less than the given space whose width is 16 inches

13.75 < 16 so the width of mirror will not fit inside the space

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