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15. Rectangle ABCD has a perimeter of 24 centimetres. Sides AB and DC are twice as long as sides AD and BC. square C Calculate the length of side AD. Do not use a ruler. cm

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15.
Rectangle ABCD has a perimeter of 24 centimetres.
Sides AB and DC are twice as long as sides AD and BC.
square 
C
Calculate the length of side AD.
Do not use a ruler.
cm

15. Rectangle ABCD has a perimeter of 24 centimetres. Sides AB and DC are twice as long as sides AD and BC. square C Calculate the length of side AD. Do not use a ruler. cm

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WarrenVeteran · Tutor for 9 years

Answer

The length of side \( AD \) will be \( x \) =4 centimeters.

Explain

## Step1: <br /><br />The perimeter of a rectangle, which is the sum of the lengths of all its four sides, can be given as twice the sum of width and height. Given this rule, we can derive an equation.<br />Given that the perimeter \( P \) is 24 cm and \( AB, DC = 2(AD, BC) \)<br /><br />## Step2:<br /><br />From the problem it's given that sides \( AB \) and \( DC \) are twice as long as sides \( AD \) and \( BC \). Forming these into an equation the perimeter constant, we get:<br /><br />### \( 2(AD + AB) = P \)<br />Here \( AD, BC \) =x (assuming the same because the length of the sides are same )<br />And \( AB, DC \) =2x<br /><br />## Step3:<br /><br />Now plug in \( x \) and \( 2x \) into the equation and solve for x:<br /><br />### \( 2(x + 2x) = 24 \)<br />which simplifies to \( 2(3x) = 24 \).<br /><br />## Step4: <br /><br />Finally, divide both sides by 6 to solve for x : <br />### \( x = \frac{24}{6} \)
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