Answer:
w = 15 cm
l = 22 cm
Step-by-step explanation:
A = w·l
w = l - 7
A = (l - 7)·l
330 = l² - 7l
l² - 7l - 330 = 0
l² + 15l - 2l - 330 = 0
l(l + 15) - 22(l + 15) = 0
(l - 22)(l + 15) = 0
l - 22 = 0 => l = 22 cm
l + 15 = 0 => l = - 15 < 0 (f)
w = l - 7 = 22 - 7 => w = 15 cm
Based on the calculations, the dimensions of the rectangle are equal to 22 cm and 15 cm.
Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Based on the information provided, we have:
Area = 330 cm²
Length = Width + 7
Substituting the parameters into the formula, we have:
330 = (W + 7)W
330 = W² + 7W
W² + 7W - 330
W² - 15W + 22W - 330
W(W - 15) + 22(W - 15)
W = 15 cm.
For the length, we have:
Length = Width + 7
Length = 15 + 7
Length = 22 cm.
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