The area of a rectangular mirror is 15 7 16 square feet. The width of the mirror is 3 1 4 feet. If there is a 5 foot tall space on the wall to hang the mirror, will it fit?

Given:

Area of rectangle = [tex]15\dfrac{7}{16}[/tex] sq. feet.

Width of the mirror = [tex]3\dfrac{1}{4}[/tex] feet.

To find:

Whether it will fit on the wall whose length is 5 foot.

Solution:

We know that, area of a rectangle is

[tex]Area=length\times width[/tex]

[tex]\dfrac{Area}{width}=length[/tex]

Substituting the given values, we get

[tex]Length=\dfrac{15\dfrac{7}{16}}{3\dfrac{1}{4}}[/tex]

[tex]Length=\dfrac{\dfrac{15\times 16+7}{16}}{\dfrac{3\times 4+1}{4}}[/tex]

[tex]Length=\dfrac{\dfrac{240+7}{16}}{\dfrac{12+1}{4}}[/tex]

[tex]Length=\dfrac{\dfrac{247}{16}}{\dfrac{13}{4}}[/tex]

[tex]Length=\dfrac{247}{16}\times \dfrac{4}{13}[/tex]

[tex]Length=4.75 [/tex]

So, length of mirror is 4.75 feet which is less than 5 feet.

Therefore, the mirror will fit on the wall.

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