Answer :
The perimeter of the glass tabletop is 232 inches. The option (E) is correct.
To find the perimeter of the glass tabletop, we need to determine its dimensions first. According to the problem, the glass tabletop is 8 inches wider than the pedestal on each side.
Dimensions of the Pedestal:
- Width: 36 inches
- Length: 48 inches
Since the tabletop extends 8 inches beyond the pedestal on each side, we add 16 inches (8 inches on each side) to both the width and the length of the pedestal.
Width of the glass tabletop:
[tex]\[ \text{Width} = 36 \, \text{inches} + 16 \, \text{inches} = 52 \, \text{inches} \][/tex]
Length of the glass tabletop:
[tex]\[ \text{Length} = 48 \, \text{inches} + 16 \, \text{inches} = 64 \, \text{inches} \][/tex]
The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[P = 2 \times (\text{Length} + \text{Width})\][/tex]
Substituting the dimensions:
[tex]\[P = 2 \times (64 \, \text{inches} + 52 \, \text{inches})\\P = 2 \times 116 \, \text{inches} = 232 \, \text{inches}\][/tex]
The correct perimeter of the glass tabletop is [tex]\( 232 \)[/tex] inches.
The complete question is:
A glass tabletop is supported by a rectangular pedestal. If the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop?
A) 92 inches
B) 116 inches
C) 176 inches
D) 184 inches
E) 232 inches
When adding make sure you add 4 sides worth of calculations.
You have to consider the left and right side (for length) and front and back
for the width.
The solution for this problem is:
Side 1 (8+36+8)
+
Side 2 (8+48+8)
+
Side 3 (8+36+8)
+
Side 4 (8+48+8)
= 232
