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Find the dimensions of the rectangle

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2 Answers

Area is equal to the length times the width.  Thus, A = L·W.  Since L = W + 3 and A = 70 cmare both given, the equation then becomes
 
70 = (W+3)W
70 = W2+3W             by distribution.  
Next, set the resulting quadratic equation equal to zero, factor, then use the zero-product property to solve for W.
 
W+ 3W - 70 = 0
(W+10)(W - 7) = 0
W = -10, 7.
Since it does not make sense that the width is negative, W must be 7 cm.  We were given the length of the rectangle was 3 more than the width, so the length, L, must be 10 cm.
Let L = the length of the rectangle and W = its width
 
Area = L*W = 70 cm2                  [The Area is 70 cm2]
L = W+3                                          [The length of a rectangle is 3 cm more than its width]
 
Substitute W+3 in place of L in the Area equation:
 
Area  = 70 cm2 = (W+3)*W             
70 = W2 + 3W
0 = W2 + 3W - 70
 
Factors to:
 
(W+10)(W-7)
W = -10 and 7
 
Can't have a negative length, so W = 7
 
Solve for L:
 
L = W + 3
L= 7 + 3
L = 10