Given:
Dante's rectangular sign has a perimeter of 96 centimeters, and the width is half of the length.
The dimensions of Megan's sign are half the dimensions of Dante's sign.
To find:
The area of Megan's rectangular sign.
Solution:
Let length of Dante's rectangular sign be x.
[tex]width=\dfrac{1}{2}x[/tex]
Perimeter of a rectangle = 2(length + width)
Perimeter of 96 centimeters. So,
[tex]2(x+\dfrac{1}{2}x)=96[/tex]
[tex]2(\dfrac{3}{2}x)=96[/tex]
[tex]3x=96[/tex]
Divide both sides by 3.
[tex]x=32[/tex]
So,
[tex]Length = 32[/tex] cm
[tex]width=\dfrac{1}{2}(32)=16[/tex] cm
The dimensions of Megan's sign are half the dimensions of Dante's sign.
So, dimensions of Megan's sign are 16 cm and 8 cm.
Area of a rectangle = length × width
Area of Megan's rectangular sign is
[tex]Area=16\times 8[/tex]
[tex]Area=128[/tex]
Therefore, the area of Megan's rectangular sign is 128 cm².
