Question

Please help!!

Answer 1

Answer:

$AC=\sqrt{13}$

Step-by-step explanation:

As the the length of the segments BC = AC, so the triangle ABC must be an isosceles triangle.

As CD ⊥ AB, it means the base AB gets bisected by CD, making two congruent angles named as ∠ACD and ∠BCD. As shown in attached figure.

CD bisecting the base AB into two equal parts means if AB = 4, then

the length of AD = 2 and the length of DB = 2. Hence, AD = DB

As BC = AC, it means these two equal sides of isosceles triangle would make equal angles on the opposite side. Hence, angle ∠A and ∠B would be equal as shown in attached figure.

As CD is bisecting the base AB into two equal parts. Hence, it can be treated as the part of two right triangles named  ACD and BCD.

So, the length of AC can be easily determined using using the Pythagoras formula.

So,

     c² = a² + b²

     $c=\sqrt{a^{2}+b^{2}}$

     $AC=\sqrt{2^{2}+3^{2}}$

     $AC=\sqrt{9+4}}$

     $AC=\sqrt{13}}$

     

Hence $AC=\sqrt{13}$

Keywords: isosceles triangle, hypotenuse, hypotenuse

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