Answer :
Answer: The length of the rectangle is 8cm while the width is 15cm.
Step-by-step explanation: The length of the rectangle has been described as 7cm less than it’s width. This means if the width is given as W, then the length would be 7 less than W, that is, length would be W - 7. Also the area has been given as 120. With this bit of information we can now express the area as follows;
Area of a rectangle = L x W
Where area is 120, length is W - 7 and width is W.
120 = (W-7) x W
120 = W^2 - 7W
We rearrange all terms on one side of the equation and we now have
W^2 - 7W - 120 = 0
What we now have is a quadratic equation, and by factorizing we now have
(W + 8) (W - 15) = 0
(W + 8) = 0 and (W - 15) = 0
Hence, either W + 8 = 0 and W = -8
OR W - 15 = 0 and W = 15.
We know that the dimensions of the rectangle cannot be a negative number, so we choose W = 15.
Having calculated that, if the length is given as W - 7, then the length is
L = 15- 7
L = 8
Therefore, the length is 8cm and the width is 15cm.
To find the dimensions of the rectangle, we use the equation for area (width times length equals 120 cm²). Solving the resulting quadratic equation, we find the width to be 15 cm and the length to be 8 cm.
The student asked about the dimensions of a rectangle where the length is 7 cm less than its width and the area is 120 cm². Let's call the width of the rectangle 'w' and the length 'w - 7 cm'.
To find the dimensions, we set up the equation for the area of a rectangle (length times width), which must be equal to 120 cm²:
w(w - 7) = 120
Multiplying out the left side gives us a quadratic equation to solve:
w² - 7w - 120 = 0
Now we factor the quadratic equation:
(w - 15)(w + 8) = 0
This gives us two possible solutions for w: w = 15 cm or w = -8 cm. Since we can't have a negative width, the width is 15 cm.
Subtracting 7 cm to get the length, we have:
length = w - 7
length = 15 - 7 = 8 cm
Therefore, the dimensions of the rectangle are 15 cm wide and 8 cm long.
