The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of th

Question

KiRa [710]

3 years ago

11

The expression 3 1/2x + 18 represents the perimeter of the rectangle shown. Write an expression that represents the length of th

e rectangle.

Mathematics

1 answer:

I am Lyosha [343] · Answer 1 · 2021-11-29T05:14:01+03:00

Length of rectangle is: $\frac{3x+8}{2}$

Step-by-step explanation:

The Perimeter of rectangle = $3\frac{1}{2}x+18$

The width of rectangle = $\frac{1}{4}x+5$

Length of rectangle = ?

The formula used to find Perimeter of rectangle is:

$Perimeter=2(L+W)$

Finding length:

$Perimeter=2(L+W)\\3\frac{1}{2}x+18=2(L+(\frac{1}{4}x+5))\\\frac{7x+18*2}{2}=2(L+(\frac{1}{4}x+5))\\\frac{\frac{7x+36}{2}}{2} =(L+(\frac{1}{4}x+5))\\\frac{7x+36}{4} =(L+(\frac{1}{4}x+5))\\L=\frac{7x+36}{4}-\frac{1}{4}x-5\\L=\frac{7x+36-x-5*4}{4}\\ L=\frac{6x+36-20}{4}\\L=\frac{6x+16}{4}\\L=2(\frac{3x+8}{4})\\L=\frac{3x+8}{2}$

So, Length of rectangle is: $\frac{3x+8}{2}$

Keywords: perimeter of the rectangle

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