Question

In ΔABC, ∠A = 90°, AB = 14 cm, AC = 48 cm. Find the

1. area of ΔABC 
2. length of perpendicular from A to BC

Answer 1

Given:

• In ΔABC, ∠A = 90°   ...(Right angle at A)
• AB = 14 cm
• AC = 48 cm

We need to find:

1. Area of ΔABC 
2. Length of perpendicular from A to BC

Stepwise calculation:

Step 1: Find BC using Pythagoras theorem

Since ∠A = 90°, triangle ABC is right angled at A, so BC is the hypotenuse.

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

= `sqrt(14^2 + 48^2)`

= `sqrt(196 + 2304)`

= `sqrt(2500)`

= 50 cm

Step 2: Find area of ΔABC

Area of a right triangle = `1/2 xx "leg"_1 xx "leg"_2`

`"Area" = 1/2 xx AB xx AC`

= `1/2 xx 14 xx 48`

= 7 × 48

= 336 cm²

Step 3: Find length of perpendicular from A to BC

Let the foot of the perpendicular from A to BC be point D. The length AD is the height from A to hypotenuse BC.

Area of ΔABC can also be expressed as:

`"Area" = 1/2 xx BC xx AD`

Solving for AD:

`AD = (2 xx "Area")/("BC")`

= `(2 xx 336)/50`

= `672/50`

= 13.44 cm

Area of ΔABC = 336 cm².

Length of perpendicular from A to BC = 13.44 cm.