The area of a rectangle is 45 square cm. If the length is 4cm greater than the width, what are the dimension of the rectangle?

Question

Eli Assouline · Accepted Answer

The length & width of rectangle are #9 and 5 # cms respectively.

Let the width of the rectangle be #x# cm; then the length will be #x+4#cm. Area of the rectangle is #x*(x+4)=45 or x^2+4x-45=0 or (x+9)(x-5)=0 :. x= -9 or x=5#Width cannot be negative. So #x=5; x+4=9:.#The length & width are #9 and 5 # cms respectively.[Ans]

Eva Adamson · Answer

undefined Let's denote the width of the rectangle as $ w $ cm. Since the length is 4 cm greater than the width, the length can be represented as $ w + 4 $ cm. The area of a rectangle is given by the formula:

$$ \text{Area} = \text{length} \times \text{width} $$

Given that the area is 45 square cm, we can set up the equation:

$$ w(w + 4) = 45 $$

Expanding the equation:

$$ w^2 + 4w = 45 $$

Rearranging terms to form a quadratic equation:

$$ w^2 + 4w - 45 = 0 $$

Now, we can factorize the quadratic equation or use the quadratic formula to solve for $ w $. After finding the value of $ w $, we can then find the length of the rectangle by adding 4 to $ w $.