A painting measuring 16×20 cm is glued on a rectangular sheet of cardboard, so that a frame of the same

| April 6, 2021 | education

A painting measuring 16×20 cm is glued on a rectangular sheet of cardboard, so that a frame of the same width is obtained. Determine the width of the frame if it is known that the area of a sheet of cardboard is 780 cm ^ 2.

1. According to the problem statement, a picture is given.

Its length is 20 cm, width is 16 cm.

It is known to be glued to a rectangular sheet of cardboard.

The result is a frame of the same width.

Let X cm be the width of the frame.

2. Then the length of the picture with the frame (20 + 2 * X) cm.

The width of the picture with a frame (16 + 2 * X) cm.

And the area of the cardboard is specified by the condition and is 780 cm2.

3. Received the equation.

(20 + 2 * X) * (16 + 2 * X) = 780.

4 * X * X + 72 * X + 320 = 780.

X * X + 18 * X – 115 = 0.

Discriminant B = 18 * 18 + 4 * 115 = 324 + 460 = 784 = 28 * 28.

X = (- 18 + 28) / 2 = 5 cm.

Answer: The width of the frame is 5 cm.



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