lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner ofan 11 in. by 20 in. piece of cardboard as shown in the diagram. She figures that for versatility the area of thebottom must be 86 in.2. What size of square should she cut from each corner?in.2The area cut from each corner should be(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)

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Asked Oct 4, 2019
lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of
an 11 in. by 20 in. piece of cardboard as shown in the diagram. She figures that for versatility the area of the
bottom must be 86 in.2. What size of square should she cut from each corner?
in.2
The area cut from each corner should be
(Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)
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lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 20 in. piece of cardboard as shown in the diagram. She figures that for versatility the area of the bottom must be 86 in.2. What size of square should she cut from each corner? in.2 The area cut from each corner should be (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.)

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Expert Answer

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Step 1

Let x be the side of the equal squares cutting by the lady from each corner of the cardboard of 11 in. by 20 in.

So, after cutting the x sides from the corner of the cardboard we have

Length of the cardboard (L) = 11-2x

Breadth of the cardboard (B) = 20 – 2x

Step 2

Since, the area of the bottom side is 86 in2.

: Area 3 L Х В
863 (11 - 2х)(20- 2х)
86 - 220- 22х - 40х + 4x2
4x2 — 62х + 134 — 0
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: Area 3 L Х В 863 (11 - 2х)(20- 2х) 86 - 220- 22х - 40х + 4x2 4x2 — 62х + 134 — 0

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Step 3

Now solving for x by qu...

-(-62)+622-4x4x134
2x4
62+ 1700
2X4
62+10 17
2X4
31+5 17
4
31+5 17
31-5 17
0r
4
4
12.9 or 2.596
12.9 then L 11 - 2 x 12.9 = -14.8 < 0
When x
Since length cannot be negative so x = 12.9 is not possible
6.740 in2
Therefore, the area cut from each corner is x2 = 2.5962
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-(-62)+622-4x4x134 2x4 62+ 1700 2X4 62+10 17 2X4 31+5 17 4 31+5 17 31-5 17 0r 4 4 12.9 or 2.596 12.9 then L 11 - 2 x 12.9 = -14.8 < 0 When x Since length cannot be negative so x = 12.9 is not possible 6.740 in2 Therefore, the area cut from each corner is x2 = 2.5962

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