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the length of a rectangle is 5√48 and its width is 4√27. What is the perimeter?​

step by step solution


Sagot :

Answer:

The perimeter is [tex]64 \sqrt{3}[/tex]

Step-by-step explanation:

Formula: P= 2(l+w)

[tex]l = 5 \sqrt{48} [/tex]

[tex]w = 4 \sqrt{27} [/tex]

[tex]p = ?[/tex]

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Find the perimeter using the formula [tex]p = 2(l + w)[/tex] .

[tex]p = 2(l + w)[/tex]

[tex]p = 2(5 \sqrt{48} + 4 \sqrt{27} )[/tex]

Simplify the rational expression [tex]5 \sqrt{48} + 4 \sqrt{27} )[/tex]

[tex]p = 2(5 \sqrt{16 \times 3} + 4 \sqrt{9 \times 3} )[/tex]

[tex]p = 2(20 \sqrt{3} + 12 \sqrt{3} )[/tex]

Add the coefficient and copy the [tex]\sqrt{3}[/tex] since they're like terms.

[tex]p = 2(32 \sqrt{3} )[/tex]

Multiply 2 by 32 and copy the [tex]\sqrt{3}[/tex]

Therefore, [tex]p = 64 \sqrt{3} [/tex]

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