Question

7. A layout artist wants to have 270 cm? of graphic art on a page that measures 20 cm by 28 cm. If the bottom border of the page must be 3 times as deep as the borders on the other three sides, how wide should each border be?

Answer 1

Answer:

• small border = 2.5 cm
• bottom border = 7.5 cm

Step-by-step explanation:

Let the width of small border = x cm

Then:

• the width of bottom border = 3x cm
• width of graphic art = (20 - x - x) cm = (20 - 2x) cm
• height of graphic art = (28 - x - 3x) cm = (28 - 4x) cm

Area of graphic art = width of graphic art × height of graphic art

$270=(20-2x)(28-4x)$

$270=2(10-x)(28-4x)$

$135=(10-x)(28-4x)$

$135=(10-x)(28-4x)$

$135=4x^2-68x+280$

$4x^2-68x+145=0$

$(2x-5)(2x-29)=0$

$x=2.5\ cm\ or\ 14.5\ cm$

Since the width of the page is 20 cm and the small border has to be less than half of the width, therefore x < 10 cm. Hence, x = 14.5 is invalid.

$\bf x=2.5\ cm$

Therefore, the small border = 2.5 cm and the bottom border = 7.5 cm.