Question

in the adjoining figure, DE ¶ BC and all measurements are in centimetres the length of AE is​

Answer 1

Step-by-step explanation:

3/4 = AE/3

AE = 9/4

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Answer 2

Answer:

Length of side AE is 9/4 cm.

Step-by-step explanation:

• Two triangles are said to be similar if two of their corresponding angles are equal and their sides are proportional.
• AA( Angle Angle similarity ) , SAS ( Side Angle Side similarity ) , SSS ( Side Side Side similarity ) are three types of similarities in triangle.

Given that :

• BC || DE
• AD = 3 cm
• DB = 4 cm
• EC = 3 cm

To find :

• Length of side AE

Solution :

• Let, the length of side AE be x cm.
• Length of side AB = AD + DB = (3 + 4) cm = 7cm
• Length of AC = AE + EC = (x + 3) cm
• Now, in ∆ABC and ∆ADE :
• ∠ ABC = ∠ ADE (corresponding angles)
• ∠ ACB = ∠ AED (corresponding angles)
• ∠ A = ∠ A
• Hence, ∆ABC is similar to ∆ADE .
• Since, ∆ABC is similar to ∆ADE, its sides are proportional to each other.

$\frac{AD}{AB} = \frac{AE}{AC} \\ \frac{3}{7} = \frac{x}{x + 3} \\ 3(x + 3) = 7x \\ 3x + 9 = 7x \\ 4x = 9 \\ x = \frac{9}{4}$

• Hence, length of side AE is 9/4 cm.