Respuesta :

CastleRook
To get the value of h we use proportionality:
ΔABC is similar to ΔADB and is similar to ΔBDC this is because they are right triangles. This implies that there corresponding sides are equal. Hence:
AD=25-16=9
using Pythagorean theorem:
c^2=a^2+b^2
then:
AB^2=(h^2+9^2)
Also:
(BC)^2=(AB)^2+(AC)^2

=25^2-(h^2+9^2)

Also:
(BC)^2=(BD)^2+(DC)^2
thus
(BC)^2=h^2+16^2
hence combing the values for (BC)^2 we get:
25^2-(h^2+9^2)=h^2+16^2
simplifying we obtain:
625-h^2-81=h^2+256
putting like terms together
625-81-256=h^2+h^2
288=2h^2
thus
h^2=144
hence
h=√144
h=12 units

The value of h is 12 , Option D is the correct answer

What is a Triangle ?

Triangle is a polygon with three sides , three angles , three vertices.

It is given in the question that

From the data given

AD=25-16=9 unit

As they are right angle Triangles ,

Applying Pythagorean theorem:

hypotenuse ² = base² + height ²

then:

AB²=   h²+9²

and

AB² +BC² = AC²

AB² +BC² = 25²

BC² = 16² + h²

AB² +16² + h²= 25²

h²+9² +16² + h²= 25²

2 h² = 288

h² = 144

h = 12

h=12 units , Option D is the correct answer .

To know more about Triangle

https://brainly.com/question/2773823

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