Question

In ΔABC, AB = 8, find a and b if a + b = 32.

Answer 1

Given: AB = 8, BC = a and AC = b

Condition: a + b = 32

△ABC is a right-angle triangle.

Step 1: Apply Pythagoras theorem:

b² = a² + 8²

= a² + 64

Step 2: Use the given relation:

a + b = 32

⇒ b = 32 – a

Substitute in the first equation:

(32 – a)² = a² + 64

Step 3: Expand and simplify:

1024 – 64a + a² = a² + 64

Cancel a² from both sides:

1024 – 64a = 64

1024 – 64 = 64a

960 = 64a

a = `960/64`

a = 15

Step 4: Find b:

b = 32 – a

= 32 – 15

= 17

∴ a = 15, b = 17