Question 631734

Please help me solve this problem:

The length of a rectangle is 7 cm more than its width. If the length is increased by 2 cm and the width increased by 4 cm, the area will be increased by 54 cm^2. Find the original length and width of the rectangle. 

Thank you so much! 


Let original width of rectangle be W
Then original length = W + 7
Increasing length by 2 makes it W + 7 + 2, or (W + 9) cm
Increasing width by 4 makes it (W + 4) cm


Original area = LW, or W(W + 7), or {{{W^2 + 7W}}}
Adjusted area = LW, or (W + 9)(W + 4), or {{{W^2 + 13W + 36}}}


Since adjusted area is increased by {{{54 cm^2}}}, then:
{{{(W^2 + 13W + 36) = (W^2 + 7W) + 56}}} 
{{{W^2 - W^2 + 13W - 7W = 56 - 36}}} 


13W - 7W = 20

6W = 20


W, or original width = {{{20/6}}}, or {{{10/3}}}, or {{{highlight_green(3&1/3)}}} cm


Original length = W + 7, or {{{3&1/3 + 7}}}, or {{{31/3}}}, or {{{highlight_green(10&1/3)}}} cm


You should be able to do the check!!


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