Question

In each of the following figure an altitude
is drawn to the hypotenuse. The length of
different segments are marked in each Figure.
Determine the value of x, y and z in each case​

Answer 1

Answer:

can you please put the figure.

Answer 2

Answer:

In a right triangle, the altitude that’s perpendicular to the hypotenuse has a special property: it creates two smaller right triangles that are both similar to the original right triangle.

(i) In △ABC, BD is altitude.

If an altitude is drawn to the hypotenuse of a right triangle as shown in the above figure, then

(AD)2=AD×AC

⇒  (x)2=4×9

⇒  x2=36

∴  x=6

Now, (BC)2=DC×AC

⇒  z2=5×9

⇒  z2=45

∴  z=35

Next, (BD)2=AD×DC

⇒  y2=4×5

⇒  y2=20

∴  y=25

(ii)  In △PQR, QS is an altitude.

If an altitude is drawn to the hypotenuse of a right triangle as shown in the above figure, then

(PQ)2=PS×PR

(6)2=4×(4+x)

36=16+4x

4x=20

∴  x=5

∴  SR=5

Now, QR2=SR×