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velikii [3]
3 years ago
14

a rectangle has length 1/2x+5 and width 1/4x+4. if the perimeter is 42 meters, what are the length and the width of the rectangl

e.
Mathematics
1 answer:
Leokris [45]3 years ago
4 0
A rectangle has 2 lengths and 2 widths that equal the perimeter.
(2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)=42 \\   \frac{(2)( \frac{1}{2x} +5)+(2)( \frac{1}{4x}+4)}{2} = \frac{42}{2}  \\  \frac{1}{2x}+ 5+ \frac{1}{4x}  +4=21 \\  \frac{1}{2x}+ \frac{1}{4x}  = 12 \\ ( \frac{1}{x} )( \frac{1}{2} + \frac{1}{4} )=12 \\ ( \frac{1}{x} )( \frac{3}{4} )=12 \\  \frac{1}{x} =16 \\ x= \frac{1}{6}  \\  \\ Length: \frac{1}{2x}+5 \\  \frac{1}{2( \frac{1}{16}) }+5 \\ 8+5=13 \\  \\ Width: \frac{1}{4x}+4 \\  \frac{1}{4( \frac{1}{16}) }  +4 \\ 4+4=8
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