Question

in triangle abc angle b =90 degree and d is a mid point of ac if ab =20cm and bd=14.5 cm find the area and the perimeter of triangle abc

Answer 1

Let the triangle be ABC in which Angle B = 90 Degree Thus it is  right angle triangle

When we draw a perpendicular BD on Side AC of the triangle, side AC gets divided into two equal parts,

Thus AD = DC
 
Now, we are Given that, AB = 20 Cm
                                       BD = 14.5 Cm
Since Angle B is 90 Degree when we draw a perpendicular from angle B Then,       Angle ABD = Angle DBC = 45 Degree

Now in triangle ABD,           Tan 45 = AD / BD
putting the value of BD,        Tan 45 = AD / 14.5
                                                  1 = AD / 14.5
Thus, AD = DC = 14.5 Cm

 Therefore Side AC = AD + DC = 14.5 + 14.5 =29 Cm

Now by Pythagoras Theorem,  In triangle ABC,
                
                                     AB^2 +BC^2 = AC^2
                                        20^2 + BC^2 = 29^2
                                                BC^2 = 841 - 400
                                                BC^2 = 441
                                                Thus, BC = 21 Cm
Now Area of Triangle ABC = 1/2 * AB * BC
                                     Area = 0.5 * 20 * 21
                                     Area = 210 Cm Sqr
          
and                    Perimeter = Ab + BC + AC 
                                           = 20 +21 + 29
                                           = 70 Cm

Answer 2

Answer:

draw perpendicular BD , Now we know that AD=DC

In tr.ABD, AB= 20 cm & BD = 14.5 cm

By PYTHAGORAS THEOREM,

AB^2 - BD^2= AD^2 (as angle ADB is 90 degree because BD is drawn perpendicular to AC)

Now , find AD with AD you know you can find AC which is 2* AD ,After that use the formula to find the area of tr.ABC = 1/2 * b * h