Question

find the length of the altitude AL of an isosceles triangle ABC where AB=AC=5cm and BC=8cm.​

Answer 1

➠ TO FIND: the altitude

➠ GIVEN:

⟹ AC = 5cm

⟹ AB = 5cm

⟹ BC = 8cm

➠ SOLUTION:

➢ Consider the above triangle.

⟹ AL+CL = BC = 8 cm

⟹ We know that, AL = CL

∴ AL = 4 cm ; CL = 4 cm

⟹ here, angle L = 90°

→ so, we will apply phythagorean theorem, according to which:

⟹ (base)²+(height)² = (hypotenuse)²

✪ Here,

⟹ base = CL = 4 cm

⟹ hypotenuse = AC = 5 cm

⟹ height = AL = let it be x

⟹ (4cm)²+(x)² = (5cm)²

⟹ 16cm²+x²= 25 cm²

⟹ x² = 25cm² - 16cm²

⟹ x² = 9cm²

⟹ x = √9cm²

∴ x = 3cm

∴ AL = 3 cm

➢ hence, the altitude AL is 3cm.