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the width of a rectangle is 3/4 the length. The perimeter of the rectangle becomes 50 cm when the the length and the width are each increased by 3 cm. Find the length and width

Sagot :

AyaZidn
[tex]w= \frac{3}{4} l[/tex]
[tex]w^{'}=w+3 [/tex]
[tex]l^{'}=l+3[/tex]

[tex]P=2( w^{'} + l^{'} )= 2((w+3)+(l+3))=2(w+l+6)=2w+2l+12[/tex]
[tex]=2*( \frac{3}{4} l)+2l+12 = \frac{3}{2} l+ \frac{4}{2} l+12=50 \\ \frac{7}{2}l =38 \\ l= \frac{38*2}{7} [/tex]

[tex]w= \frac{3}{4} l= \frac{3}{4} * \frac{38*2}{7} = \frac{19*3}{7} [/tex]

Serynneidn
w= (3/4)l
2(l+3)+2(w+3)=50
multiply out
2l+6+2w+6=50
replace the w with the equation for w at the top and combine like terms
2l+2(3/4)l+12=50
multiply out
2l+3/2l+12=50
combine like terms and subtract 12 from both sides
7/2l=38
divide both sides by 7/2
l=76/7
find w
w=3/4l
w=(3/4)(76/7)
w=57/7
length= 76/7 or 10.86 cm
width= 57/7 or 8.14 cm

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