Question 171692
Let x=width and y=height



"The perimeter of a picture frame is 11 feet" translates to {{{11=2x+2y}}}. Note: remember, the perimeter formula is {{{P=2L+2W}}} where L and W are the length and width



"three times the height is equal to eight times the width" translates to {{{3y=8x}}}



{{{3y=8x}}} Start with the second equation



{{{y=(8x)/3}}} Divide both sides by 3 to isolate y



{{{11=2x+2y}}} Go back to the first equation



{{{11=2x+2((8x)/3)}}} Plug in {{{y=(8x)/3}}}



{{{11=2x+(16x)/3}}} Multiply



{{{3(11)=3(2x)+cross(3)((16x)/cross(3))}}} Multiply EVERY term by the LCD 3 to clear the fraction.



{{{33=6x+16x}}} Multiply and simplify



{{{33=22x}}} Combine like terms.



{{{33/22=x}}} Divide both sides by 22 to isolate "x"



{{{3/2=x}}} Reduce



So the first answer is {{{x=3/2}}} (which in decimal form is {{{x=1.5}}})




{{{y=(8x)/3}}} Go back to the isolated equation



{{{y=(8(3/2))/3}}} Plug in {{{x=3/2}}}



{{{y=(12)/3}}} Multiply 8 and {{{3/2}}} to get {{{8(3/2)=24/2=12}}}



{{{y=4}}} Reduce



So the second answer is {{{y=4}}}




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Answer:



So the answers are {{{x=3/2}}} (which in decimal form is {{{x=1.5}}}) and {{{y=4}}}



This means that the width is 1.5 feet and the height is 4 feet.