A white rectangle, which is 9 cm long and 6 cm wide, is glued onto the green one so that a green frame
August 30, 2021 | education|
A white rectangle, which is 9 cm long and 6 cm wide, is glued onto the green one so that a green frame of the same width is formed. Find the width of the frame if the area of the green rectangle is 130 cm2
a = 9 cm.
b = 6 cm.
S = 130 cm ^ 2.
Let’s say that the width of the green frame that is formed is x cm.
The length of the green rectangle will be (a + 2 * x), the width (b + 2 * x).
Let us express the area of the green rectangle.
(a + 2 * x) * (b + 2 * x) = S.
(9 + 2 * x) * (6 + 2 * x) = 130.
54 + 12 * x + 18 * x + 4 * x ^ 2 = 130.
4 * x ^ 2 + 30 * x – 76 = 0.
Let’s solve the quadratic equation.
D = 30 ^ 2 + 4 * 4 * 76 = 2116.
x1,2 = (- 30 ± √2116) / 2 * 4.
The negative root cannot be long.
x = 16/8 = 2 cm.
Answer: The width of the green frame is 2 cm.
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