Problem: You are an engineer designing the lot for a dream home. The lot has a rectangular shape, and the length is 10 meters longer than the width. The total area of the lot is 180 square meters. Determine the dimensions of the lot
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Problem: You are an engineer designing the lot for a dream home. The lot has a rectangular shape, and the length is 10 meters longer than the width. The total area of the lot is 180 square meters. Determine the dimensions of the lot
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Answer:
The total area of the lot is given as 180 square meters, so we can write the equation:
Area = Length × Width
180 square meters = (W + 10) meters × W meters
Now, we can solve for the width (W). First, expand the equation:
180 = W(W + 10)
Next, distribute W on the right side of the equation:
180 = W^2 + 10W
Now, we have a quadratic equation. To solve for W, we can set it equal to zero:
W^2 + 10W - 180 = 0
To factor this quadratic equation, we look for two numbers that multiply to -180 (the product of the coefficients of W^2 and the constant term) and add up to 10 (the coefficient of the middle term, 10). These numbers are 20 and -10:
(W + 20)(W - 10) = 0
Now, set each factor equal to zero and solve for W:
W + 20 = 0
W = -20 (We discard this solution because width cannot be negative in this context.)
W - 10 = 0
W = 10 meters
So, the width of the lot is 10 meters, and the length (W + 10) is 20 meters. Therefore, the dimensions of the lot are 10 meters by 20 meters.
Step-by-step explanation: