Question

Dante and Megan are each making a rectangular sign. Dante's 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. What is the area of Megan's rectangular sign? Enter the answer in the box.​

Answer 1

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.

$width=\dfrac{1}{2}x$

Perimeter of a rectangle = 2(length + width)

Perimeter of 96 centimeters. So,

$2(x+\dfrac{1}{2}x)=96$

$2(\dfrac{3}{2}x)=96$

$3x=96$

Divide both sides by 3.

$x=32$

So,

$Length = 32$ cm

$width=\dfrac{1}{2}(32)=16$ 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

$Area=16\times 8$

$Area=128$

Therefore, the area of Megan's rectangular sign is 128 cm².