SOLUTION: the length of a rectangle is 3 cm more than the width. the area is 70cm^2. find the demensions of the rectangle

Question 259504: the length of a rectangle is 3 cm more than the width. the area is 70cm^2. find the demensions of the rectangle
Answer by mathbath(13) (Show Source): You can put this solution on YOUR website!
Let the length of the rectangle be "L" and Width be "B".
From the problem we know that L is 3cm more than B. So if we put it in the form of an equation,
L = B + 3 --> (1)
The formula to calculate the area of a rectangle is..
A = L * B
where A = Area of the rectangle
L = Length of the rectangle
B = Breadth of the rectangle
Now from the problem we have the following values..
A = 70
L = B + 3 -->(From (1) above )
Substituting these values in the above formula..
70 = (B + 3) * B
70 = B*B + 3*B
70 - 70 = B^2 + 3B - 70 -->(Subtracting 70 from both sides)
0 = B^2 + 3B - 70
0 = B*B + (10B - 7B) - (10 * 7) --->(Since 10B - 7B = 3B and 10*7 = 70)
0 = B(B + 10) - 7(B + 10) --> (Taking out the common figures which are "B" and "-7" )
0 = (B + 10)(B - 7) -->(Since (B + 10) is common )
So we have the following conclusions from above,
B + 10 = 0 OR B - 7 =0
B = -10 OR B = 7
Now since B represents the width of the rectangle it cannot be negative. So the correct answer would be B = 7
So the breadth of the rectangle is 7cm
From (1) above we know that,
L = B + 3
Substituting the value for B..
L = 7 + 3
L = 10
So the length of the rectangle is 10cm
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