What is the value of h in the figure below? In this diagram bad~ CBD

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

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step-by-step explanation: