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Alika [10]
2 years ago
9

A rectangular painting is to have a total area (including the frame) of 1200 cm2. If the painting is 30 cm long and 20 cm wide,

find the width of the frame
Mathematics
1 answer:
Leno4ka [110]2 years ago
3 0

Answer:

5 cm

Step-by-step explanation:

Let x = width of frame.

The width of the frame is added all around the painting, so you must add 2x to the length of the painting and 2x to the width of the painting to find the total length and width including the frame.

painting length: 30

total length: 2x + 30

painting width: 20

total width: 2x + 20

total area = LW

total area = (2x + 30)(2x + 20)

total area = 1200

(2x + 30)(2x + 20) = 1200

(x + 15)(x + 10) = 300

x^2 + 10x + 15x + 150 = 300

x^2 + 25x - 150 = 0

(x - 5)(x + 30) = 0

x - 5 = 0  or  x + 30 = 0

x = 5  or x = -30

The width of the frame cannot be a negative number, so we discard the solution x = -30.

Answer: 5 cm

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Step-by-step explanation:

We need the formula for arc length (in radians) to solve this problem. The formula is:

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In this diagram, we can see that  \theta  is beign intercepted by the big arc with measure 20 cm. So arc length, s, is 20

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