Question

the base the base of a triangle is 4cm longer than its altitude if the area of the triangle is 48 square CM then find its base and altitude ​

Answer 1

Answer:

★ Base = 12 cm ★

★ Altitude = 8 cm ★

Step-by-step explanation:

Given:

• Base of triangle is 4 cm longer than it's altitude.
• Area of triangle is 48 cm².

To Find:

• Length of base and altitude

Solution: Let the length of altitude be x cm .

∴ Length of Base will be x + 4 cm

★ Area of Triangle = 1/2 x ( Base x Height ) ★

$\small\implies{\sf }$ Area of triangle = 1/2(x + 4) ( x )

$\small\implies{\sf }$ 48 = 1/2 (x)² + 4x

$\small\implies{\sf }$ 48 = 1/2 (x)² + 4x

$\small\implies{\sf }$ 48 x 2 = x² + 4x

$\small\implies{\sf }$ 96 = x² + 4x

$\small\implies{\sf }$ 0 = x² + 4x – 96

★ By middle term splitting ★

$\small\implies{\sf }$ x² + 4x – 96

$\small\implies{\sf }$ x² + 12x – 8x – 96

$\small\implies{\sf }$ x (x + 12) – 8 (x + 12)

$\small\implies{\sf }$ (x + 12) (x – 8)

† Either x + 12 = 0 or x – 8 = 0

→ x = –12 or x = 8

→ x = 8 [ Negative ignored because it cannot be negative ]

Therefore, Length of altitude = x = 8 cm and Length of base = x + 4 = 8 + 4 = 12 cm.

_________________________

★ Check ★

→ 1/2 ( Base x Height ) = 48 cm²

→ 1/2 ( 12 x 8 ) = 48 cm²

→ 96/2 = 48 cm²

→ 48 cm² = 48 cm² LHS = RHS