Question

If in an equilateral triangle ABC, AD is median and in AABD, AE is median, then AB2: AEP will be (1) 15:16 (2) 18:17 L (3) 16:13 (4) 15:14 In an equilateral triangle, the ratio of the sum of GNE​

Answer 1

Answer:

the answer is 15:16

Step-by-step explanation:

hope it helps✨✨

Answer 2

The correct answer is 16:13

GIVEN

ABC is an equilateral triangle.

AD is the median of ∆ABC

AE is the median of ∆ABD

TO FIND

$\frac{AB^{2} }{ {AE}^{2}}$

SOLUTION

We can simply solve the above problem as follows.

We know that the Median of an equilateral triangle is always perpendicular bisector to the corresponding side.

So,

AD | BC

Let the sides of the equilateral triangle = x

So,

AB=BC=AC = x cm

BD = DC = x/2

In ∆ABD

AE is the median

Therefore,

BE = ED = x/4 cm

Applying Pythagoras theorem In right angle ∆ABD

${AB}^{2} = {BD}^{2} + {AD}^{2}$

${x}^{2} = ( \frac{x}{2} )^{2} + {ad}^{2}$

${AD}^{2} = {x}^{2} - \frac{ {x}^{2} }{4}$

${AD}^{2} = \frac{3}{4} {x}^{2}$

Applying Pythagoras theorem in ∆AED

${AE}^{2} = {ED}^{2} + {AD}^{2}$

${AE}^{2} = \frac{ {x}^{2} }{16} + \frac{3}{4} {x}^{2}$

${AE}^{2} = \frac{13 {x}^{2} }{16}$

Now,

$\frac{ {AB}^{2} }{ {AE}^{2} } = \frac{ {x}^{2} }{ \frac{13 {x}^{2} }{16} }$

= 16/13

${AB}^{2} : {AE}^{2} = 16:13$

Hence, The correct answer is 16:13

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