Question

URGENT!! A​ solid-gold jewelry box was found in the underwater palace of Cleopatra just off the shore of Treasure City. The length of the rectangular box is 21 centimeters less than triple the width. The perimeter of the box is 230 centimeters. Find the length and width of​ Cleopatra's solid-gold jewelry bo

Answer 1

To find the dimensions of Cleopatra's solid-gold jewelry box with a perimeter of 230 cm and the length being 21 cm less than triple the width, we calculate the width as 34 cm and the length as 81 cm.

Step-by-step explanation:

To solve for the dimensions of Cleopatra's solid-gold jewelry box, we'll use the information provided about the perimeter and the relationship between the length and the width. Let's let w represent the width of the box, then the length l would be 3w - 21 centimeters. The formula for the perimeter P of a rectangle is P = 2l + 2w. Substituting the known values:

• The perimeter P is given as 230 cm.
• The length l in terms of width w is 3w - 21 cm.

Now we can set up the equation:

230 = 2(3w - 21) + 2w

Expanding this, we get:

230 = 6w - 42 + 2w

Combining like terms:

8w - 42 = 230

Add 42 to both sides:

8w = 272

Divide both sides by 8:

w = 34

Now that we have the width, we can find the length:

l = 3(34) - 21

l = 102 - 21

l = 81

Therefore, the width of Cleopatra's solid-gold jewelry box is 34 centimeters and the length is 81 centimeters.

Answer 2

Width = 34 cm

Length = 81 cm

Step-by-step explanation:

Let length be l and width be w

Let perimeter be p or p = 2(l+w)

The length of the rectangular box is 21 centimeters less than triple the width:

This means

l = 3w - 21

Also, perimeter is 230, so

2(l+w) = 230

or

l+w = 115

Putting equation 1 in this equation, we get:

l+w=115

(3w - 21)+w=115

Solving:

`(3w - 21)+w=115\\4w=136\\w=34`

To find length:

l = 3w - 21

l = 3(34) - 21

l = 81

Hence

Width = 34 cm

Length = 81 cm