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Question

The perimeter of a rectangle ABCD is 36 cm. If AB = CD and AD = BC and the measure of BC is twice the measure of AB. Find the measure of AB and BC.

A
AB = 6 cm and BC = 12 cm
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B
AB = 12 cm and BC = 12 cm
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C
AB = 12 cm and BC = 6 cm
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D
AB = 4 cm and BC = 15 cm
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Solution

The correct option is A AB = 6 cm and BC = 12 cm

ABCD is a rectangle.
AB = CD and AD = BC (Given)

Let the measure of AB = b.
Measure of BC = 2 AB (Given)
Hence, BC = 2b.

Perimeter = AB +BC + CD + DA = 36
b + 2b + b + 2b = 36
6b = 36
b =366 = 6

AB = b = 6 cm
BC = 2b = 12 cm
The measure of AB and BC are 6 cm and 12 cm respectively.

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