3. a) The dimensions of your game cover are 20 cm x 15 cm. However, you need to have a strip of

Mathematics

2 answers:

DaniilM [7]3 years ago

6 0

20cm×15 cm =300

/100 = 0.32

yuradex [85]3 years ago

5 0

9514 1404 393

Answer:

1.5 cm

Step-by-step explanation:

All areas are in cm^2. For a width w, the border will have an area equal to the product of its centerline length and its width:

border area = 2((20-w) +(15-w))·w = w(70 -4w)

This area is 32% of the total cover area, so is ...

0.32(20)(15) = 96

Equating these expressions for the area gives ...

96 = 70w -4w^2

w^2 -17.5w = -24 . . . . . divide by -4

w^2 -17.5w +8.75^2 = -24 +8.75^2 . . . . . complete the square

(w -8.75)^2 = 52.5625 . . . . simplify

w -8.75 = ±√52.5625 = ±7.25

A border width only makes sense if it is between 0 and 7.5 cm, so the appropriate value for w is ...

w = 8.75 ± 7.25 . . . . . . . . . add 8.75

w = 8.75 -7.25 = 1.50 . . . . . the solution w=16 makes no sense

The border width is 1.5 cm.

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IrinaK [193]

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