Find the dimensions of the rectangle

Question

_{the length of a rectangle is 3cm more than the width the area is 70cm²}

Answer 1

Area is equal to the length times the width.  Thus, A = L·W.  Since L = W + 3 and A = 70 cm² are 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.

 

W² + 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.

Answer 2

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