Question

Please answer the first one...will mark as brainliesttttt....

Answer 1

I'll assume that D and E are midpoints of BC and AC respectively.

AC=2AE=4 so AE=2

BC=2BD=3 so BD=1.5

Let P be the intersection point of AD and BE. Note that P is the centroid.

Because AD and BE are medians, we know that:

BP=2PE and AP=2PD

I just used a property that says that the centroid divides each median in the ratio 2:1. The proof isn't hard, you can find several videos explaining it (for example: Khan Academy).

In order to simplify the notation:

BP=2n , PE=n , AP=2m , PD=m and AB=x

△EPA , △BPD and △APE are right angled at P. Now we can use the Pythagorean Theorem:

(I): (2m)2+n2=22=4

(II): (2n)2+m2=1.52=2.25

(III): (2m)2+(2n)2=x2

You can solve (I) and (II) to find the values of m and n. I solved 4(II)−(I) to find n, there are many different methods. So now we know that:

n2=13 and m2=1112

Let's solve (III):

x2=(2m)2+(2n)2=4m2+4n2

x2=4⋅1112+4⋅13=113+43=153=5

There are two solutions:

x=±5–√5

But AB is a segment, the length of a segment is always positive:

x=AB=5–√5

And we are done!