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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 23 centimeters less than triple the width. The perimeter of the box is 190 centimeters. Find the length and width of Cleopatra solid gold jewelry box.

Sagot :

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 23 centimeters less than triple the width. The perimeter of the box is 190 centimeters. Find the length and width of Cleopatra solid gold jewelry box.​

we have that

the perimeter of a rectangle is equal to

P=2(L+W)

we have

P=190 cm

so

190=2(L+W)

simplify

95=L+W -----> equation A

and

L=3W-23 ----> equation B

solve the system

substitute equation B in equation A

95=(3W-23)+W

solve for W

95=4W-23

4W=95+23

4W=118

W=29.5 cm

Find the value of L

L=3(29.5)-23

L=65.5 cm

therefore

Length is 65.5 cm

Width is 29.5 cm

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