Question

in the figure the value of ab/bc + bd/ad=​

Answer 1

Answer:

From the figure the value of $\dfrac{AB}{BC}+\dfrac{BD}{AD}=3$

Step-by-step explanation:

The question is to find the value of $\frac{AB}{BC} +\frac{BD}{AD}$ from the given figure. WE have given a figure of triangle ABC, inside the triangle we can see another triangle ABD.

From the figure, we can conclude that it is a right-angle triangle, that is $\angle B=90^{\circ }$ on both triangles. One of the angles is given on both triangles. The given angles in the triangles ABC and ABD are,

    $<BAC=45^{\circ }$ and $\angle BAD=30^{\circ }$

The sum of the three angles of a triangle is 180 degrees. Then,

    $\angle ACB=180^{\circ}-(90^{\circ }+45^{\circ })=45^{\circ}$

    $\angle ADB=180^{\circ }-\left(30^{\circ}+90^{\circ}\right)=60^{\circ}$

So the angles of the triangle ABC are $90^{\circ},45^{\circ},\ and\ 45^{\circ}$. Then the length of a $90^{\circ},45^{\circ},\ and\ 45^{\circ}$ triangle can solve by the Pythagorean theorem. According to the theorem, the ratio of the sides of the triangle is,

$AB:BC:AC=1:1:\sqrt{2}$

∴ $\dfrac{AB}{BC} =\dfrac{1}{1}=1$

The angles of the triangle ABD are $90^{\circ},60^{\circ},\ and\ 30^{\circ}$. And the length the sides of this triangle can also solve by the Pythagorean theorem. Then according to the theorem, the ratio of the sides of the triangle is,

$AB:BD:AD=\sqrt{3}:1:2$

∴  $\dfrac{BD}{AD} =\dfrac{2}{1}=2$

Then,

       $\dfrac{AB}{BC}+\dfrac{BD}{AD}=1+2=3$

So this is the answer to the question.

Answer 2

Step-by-step explanation:

correct answer to this question is 3/2