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.

AB = 6 cm and BC = 12 cm

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AB = 12 cm and BC = 12 cm

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AB = 12 cm and BC = 6 cm

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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
$\to$ b + 2b + b + 2b = 36
$\to$ 6b = 36
$\to$ b = $\frac{36}{6}$ = 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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Similar questions

Construct a quadrliateral ABCD; if:

(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and $∠$ ABC = $75^{\circ}$ .

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and $∠ BCD = 60^{\circ}$

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, $∠ A = 60^{\circ}$ and $∠ B = 75^{\circ}$ .

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, $∠ B = 75^{\circ}$ and $∠ C = 120^{\circ}$

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

△ A B C

A B = 6 \sqrt{3} c m, A C = 12 c m

B C = 6 c m

∠ B

Find the Length of all sides of the given right angled triangle if the area is 36 $c m^{2}$

A B ∥ C D

A D = B C = 5 c m, A B = 12 c m

C D = 7 c m

A B = B C

A D = \frac{1}{2} C D

A D = \frac{1}{4} A B

B C = 12

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