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.

Answer 1

SOLUTION

GIVEN

• Dante and Megan are each making a rectangular sign.

• Dante's sign has a perimeter of 96 centimeters

• The width is half of the length.

• The dimensions of Megan's sign are half the dimensions of Dante's sign.

TO DETERMINE

The area of Megan's rectangular sign

EVALUATION

Here it is given that

Dante and Megan are each making a rectangular sign.

The width is half of the length

Let length = 2a cm and width = a cm

Then perimeter

= 2( 2a + a ) cm

= 6a cm

Dante's sign has a perimeter of 96 centimeters

$\sf{6a = 96}$

$\sf{ \implies \: a = 16}$

So length of Dante's rectangular sign = 32 cm and width = 16 cm

Now it is given that the dimensions of Megan's sign are half the dimensions of Dante's sign.

So length of Megan's rectangular sign = 16 cm and width = 8 cm

Hence the area of Megan's rectangular sign

= 16 cm × 8 cm

$\sf{ = 128 \: \: {cm}^{2} }$

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