Question

In triangle ABC, AB=26cm,BC=28cm,and the altitude AD=24cm. Calculate AC.

Answer 1

it is given that in a triangle ABC,

AB=26 cm,

BC=28 cm,

altitude(height)=24 cm

then AC value can be calculated by,

let AD the altitude be a median which divides BC into half so,

BC=DC + BD

DC = 14 cm

now we get two right triangles ABD and ADC

IN A RIGHT TRIANGLE ADC we have,

AC^2 =AD^2 + DC^2

AC^2 = 24^2 + 14^2

AC^2= 576+196

        = 772

AC        =  square root of 772

             = 27.8 cm

Answer 2

Answer:

answer is 30 cm ( also in books answersheet)

Step-by-step explanation:

triangle ABC, let Ad a altitude between BC

so there will be a triangle ABD

in triangle ABD = AB =26 cm

AD=24 cm

BD = ?

BD =AB”2-AD 2. (by Pythagoras theorem)

=26 -24 cm "2. ("2 means square)

= 676 - 576 cm

BD "2= 100cm = BD =10 cm

Now Dc =? DC =BC -BD

28-10cm

18 cm = Dc

by making altitude we get two right angles

ADB AND ADC

AC = AD"2+DC"2. (by Pythagoras theorem)

=24 + 18cm "2

=576 + 324 cm

Ac"2 =900cm

AC= 30 cm

this will help you