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