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Answer :
Answer:
the width is 8cm
Step-by-step explanation:
8x15=120
8(width)+7cm=15(length)
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To find the width of the rectangle, a quadratic equation is formulated with the width represented as 'w' and the length as 'w + 7 cm' given the length is 7 cm longer. The area equation 120 = w^2 + 7w is solved to find that the width w = 8 cm, as lengths cannot be negative.
The problem given is a typical quadratic equation application, where we are dealing with the dimensions of a rectangle and the area it encloses. To find the width of the rectangle, we can let the width be represented by w and the length will then be w + 7 cm, since it is stated that the length is 7 cm longer than its width. We know that the equation for the area (A) of a rectangle is given by
A = length × width
Therefore, we can set up the following equation:
A = (w + 7) × w
Given that the area is 120 cm², we can substitute and obtain the quadratic equation:
120 = w² + 7w
Rearranging the equation, we get:
w² + 7w - 120 = 0
Solving this quadratic equation either by factoring or using the quadratic formula, we find that w = 8 cm or w = -15 cm. Since the width cannot be negative, the rectangle's width is 8 cm.
The length of the rectangle would therefore be 8 cm + 7 cm = 15 cm.
