Question

Find the area ot triangle are 80cm, 48cm, and 64cm.also find the altitude corresponding to the sides of length 64cm

Answer 1

Answer:

★ Area = 1536 cm² ★

★ Altitude = 48 cm² ★

Step-by-step explanation:

Given:

• Sides of triangle are 80, 48cm and 64cm.

To Find:

• Area of the triangle and also the height of Altitude.

Solution: Let in ∆ABC

• AB = 48 cm
• BC = 64 cm
• AC = 80 cm
• AD = Altitude

★ We have to find Area of ∆ABC by using Heron's formula ★

† Heron's Formula = √s (s–a) (s–b) (s–c)

• S = Semi Perimeter and
• S = (a + b + c/2)

$\small\implies{\sf }$ S = (48 + 64 + 80/2)

$\small\implies{\sf }$ S = (192/2)

$\small\implies{\sf }$ S = 96

Now, Put the value of S in formula

$\small\implies{\sf }$ Area of ∆ABC = √96 (96–48) (96–64) (96–80)

$\small\implies{\sf }$ Area of ∆ABC = √96 x 48 x 32 x 16 [ Do prime Factorisation ]

$\small\implies{\sf }$ Area of ∆ABC=√2x2x2x2x2x3x2x2x2x2x3x2x2x2x2x2x2x2x2x2

$\small\implies{\sf }$ Area of ∆ABC = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

$\small\implies{\sf }$ Area of ∆ABC = 1536 cm²

Hence, Area of triangle ABC is 1536 cm².

★ Again, Area of Triangle = 1/2(base x Height)★

$\small\implies{\sf }$ Area of ∆ABC = 1/2( BC x AD )

$\small\implies{\sf }$ 1536 = 1/2( 64 x AD )

$\small\implies{\sf }$ 1536 = 32 x AD

$\small\implies{\sf }$ 1536/32 = AD

$\small\implies{\sf }$ 48 cm = AD

Hence, The length of AD or Altitude of triangle ABC is 48 cm