Question

in a triangle ABC, angel B=90°, AC=16cm,BC=8cm and B is perpendicular to AD, area of triangle ADB​

Answer 1

Assuming the above illustration is an accurate representation of the question, our task is to find the length of CD.

By definition, since triangles ABC and CBD each have a right angle and share angle B, then their third angles (A for the larger, angle DCB for the smaller) must be equal making them similar triangles. The ratios of corresponding sides in similar triangles are all equal, so all we need to do is set up a proportion using the ratio of the long legs (CA, a known, and CD, our mystery length) to find our unknown.

Hypotenuse (large) Long Leg (large)

____________________ = _________________

Hypotenuse (small) Long Leg (small)

becomes

20 . . 16

___ = ___

12 . . x

To solve a proportion, cross-multiply and then divide:

12 x 16 = 192 and 192 / 20 = 9.6 is our unknown x

Answer 2

Answer:

Area of right triangle = 1/2 b×h

Given ,

Hypotenuse,AC = 16 cm

Base, BC = 8 cm

By Pythagoras theorem,

(AC)^2 = (BC)^2 + (AB)^2

256 = 64 + (AB)^2

(AB)^2 = 192

(AB) = √192

AB = 8√3 cm

Therefore height or perpendicular,AB = 8√3 cm

Area of right triangle = 1/2 b×h

= 1/2 (8×8√3)

= 1/2 (64√3)

= 32√3 cm^2

HOPE IT HELPS YOU.