Question

In isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of the altitude from A on BC is

Answer 1

Fig. Attachment for solutions :-

$\mathcal{\huge{\fbox{\red{Question\:?}}}}$

✴ In isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of the altitude from A on BC is. ?

$\mathcal{\huge{\fbox{\green{AnSwEr:-}}}}$

✏ The measure of the altitude from A on BC is 24 cm.

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

• In isosceles triangle ABC.

• AB = AC = 25 cm and BC = 14 cm .

To Find :-

The measure of the altitude from A on BC.

Calculation :-

We have a given triangle △ABC.

AB = AC = 25 cm & BC = 14 cm

In ΔABD and ΔACD,

• ∠ADB = ∠ADC [Right angles]

• AB = AC [Same measure]

• AD = AD. [common ]

Then ΔABD and ΔACD are congruent (BY R.H.S)

Hence, BD = CD =7cm. (cpct)

Using Pythagoras theorem,

AD² +BD² =AB²

⇒AD² +7² =25²

⇒AD² =625−49=576

⇒AD=24cm

Hence, The measure of the altitude from A on BC is 24 cm.

___________________________________

Answer 2

Answer :-

Given Data :-

• △ABC,

• AB = AC = 25 cm

• BC = 14 cm

To Get :-

• The altitude from A on BC is

Calculating :-

Let the altitude be AD or BC.

• AC=25 cm
• AB=25 cm
• BC=14 cm

∴ DC= 1/2×BC

= 1/2×14=7cm

By Pythagoras theorem,

AD² +CD² =AC²

⇒AD² +7² =25²

⇒AD² =625−49=576

⇒AD=24cm

®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®