O c.
O d.
47. An isosceles right triangle has area 8 sq.cm. The lenghth of its
hypotenuse is
Answers
Answer:
✬ Hypotenuse = 4√2 cm ✬
Step-by-step explanation:
Given:
Area of isosceles right angled triangle is 8 cm².
To Find:
What is the length of hypotenuse ?
Solution: Let ABC be a isosceles right angled triangle. We know that in a isosceles triangle opposite sides and opposite angles are equal.
Here in ABC, we have
AB = Perpendicular or height
BC = Base
AB = BC
Let assume that height = base = x.
★ Area of ∆ = 1/2(Base)(Height) ★
\implies{\rm }⟹ 8 = 1/2(AB)(BC)
\implies{\rm }⟹ 8 = 1/2(x)(x)
\implies{\rm }⟹ 8 = x²/2
\implies{\rm }⟹ 16 = x²
\implies{\rm }⟹ √16 = x
\implies{\rm }⟹ 4 cm = x
So, Meaure of perpendicular and base of isosceles triangle is of 4 cm.
[ Now by Pythagoras Theorem in ∆ABC ]
➭ AC² = AB² + BC²
➭ AC² = 4² + 4²
➭ AC² = 16 + 16
➭ AC² = 32
➭ AC = √32 = 4√2
Hence, the length of hypotenuse is 4√2 cm.
Answer:
Answer:
✬ Hypotenuse = 4√2 cm ✬
Step-by-step explanation:
Given:
Area of isosceles right angled triangle is 8 cm².
To Find:
What is the length of hypotenuse ?
Solution: Let ABC be a isosceles right angled triangle. We know that in a isosceles triangle opposite sides and opposite angles are equal.
Here in ABC, we have
AB = Perpendicular or height
BC = Base
AB = BC
Let assume that height = base = x.
★ Area of ∆ = 1/2(Base)(Height) ★
\implies{\rm }⟹ 8 = 1/2(AB)(BC)
\implies{\rm }⟹ 8 = 1/2(x)(x)
\implies{\rm }⟹ 8 = x²/2
\implies{\rm }⟹ 16 = x²
\implies{\rm }⟹ √16 = x
\implies{\rm }⟹ 4 cm = x
So, Meaure of perpendicular and base of isosceles triangle is of 4 cm.
[ Now by Pythagoras Theorem in ∆ABC ]
➭ AC² = AB² + BC²
➭ AC² = 4² + 4²
➭ AC² = 16 + 16
➭ AC² = 32
➭ AC = √32 = 4√2
Hence, the length of hypotenuse is 4√2 cm.