Question

ABC is a triangle in which AB = AC = 4 cm and ZA = 90°. Calculate the area of ABC . Also find the length of perpendicular from A to BC.
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Answer 1

Step-by-step explanation:

Area of triangle ABC = 1/2 ×BASE × HEIGHT

= 1/2 × AB × AC

= 1/2 × 4× 4

= 2 × 4

= 8 cm square

LET AD IS PERPENDICULAR TO BC

In Triangle ADB AND ADC

AD = AD ( common)

angle ADC = angle ADB ( each 90 degree)

AB = AC (Given)

Triangle ADB (congruent to). triangle ADC ( RHS criteria)

BD = CD ( cpct )

in triangle ABC , BY Pythagoras theorem

ABsquare + ACsquare = BC square

4 square +4 square = BCsquare

16 +16 = BCsquare

32 = BC square

:. BC = 4√2 cm

BD + CD = BC

2BD = BC (. BD = CD )

2BD = 4√2

BD = 2√2 cm

now in triangle BAD , by Pythagoras theorem

ADsquare + BD square = ABsquare

ADsquare + 2√2 square = 4 square

ADsquare + 4×2 = 16

ADsquare + 8 = 16

ADsquare = 16- 8

ADsquare = 8

.: AD = √8

.: AD = 2√2 cm

Hence length of perpendicular from A to BC = length of AD = 2√2 cm

Hope this helps

Answer 2

Given :-

AB = AC = 4 cm

Angle A = 90°

(In the Attachment)

Let ∆ABC be the given triangle and h be the length of altitude AD.

Then draw AD Perpendicular To BC.

Therefore, BD = ½BC

Now,

BC² = AB² + AC²

BC² = (4)² + (4)²

BC² = 16 + 16

BC = √32

BC = 5.65 cm

So,

BD = ½BC = ½ × 5.65 = 2.825 cm

Now,

AB² = AD² + BD²

(4)² = h² + (2.825)²

16 = h² + 7.980625

h² = 16 - 7.980625

h = √8.091675

h = 2.84 cm

Area a = ½ × b × h

= ½ × BC × AD

= ½ × 5.65 × 2.84

= 8.02 cm²

= 8 cm² [Estimation]

Length of perpendicular A to BC :

AD = 2.84 cm