Find the perimeter of an isosceles right triangle having an area of 100cm^2
Answers
Answer:
48.28 cm
Step-by-step explanation:
Step-by-step explanation:
We are given an isosceles right angled triangle .
Since it is an isosceles triangle .So, its two sides must be equal
Since it is a right angles triangle So, the two sides that must be equal are Perpendicular and Base.
Let the perpendicular be x
So, perpendicular = base =x
Area of triangle =\frac{1}{2} \times base \times height
2
1
×base×height
Since we are given that the area is 100 sq.cm
So, 100=\frac{1}{2} \times x \times x100=
2
1
×x×x
200=x^2200=x
2
\sqrt{200}=x
200
=x
So, perpendicular = base = √200 cm = 10√2 cm
Now to find hypotenuse we will use Pythagoras theorem:
Hypotenuse^2=Perpendicular^2+Base^2Hypotenuse
2
=Perpendicular
2
+Base
2
Hypotenuse^2=(\sqrt{200})^2+(\sqrt{200})^2Hypotenuse
2
=(
200
)
2
+(
200
)
2
Hypotenuse^2=200+200Hypotenuse
2
=200+200
Hypotenuse^2=400Hypotenuse
2
=400
Hypotenuse=\sqrt{400}Hypotenuse=
400
Hypotenuse=20Hypotenuse=20
So, perimeter = Sum of all sides
=10\sqrt{2}+10\sqrt{2}+2010
2
+10
2
+20
=20\sqrt{2}+2020
2
+20
=48.28cm48.28cm
Hence the perimeter of triangle is 48.28 cm
Answer:
Answer:
48.28 cm
Step-by-step explanation:
Step-by-step explanation:
We are given an isosceles right angled triangle .
Since it is an isosceles triangle .So, its two sides must be equal
Since it is a right angles triangle So, the two sides that must be equal are Perpendicular and Base.
Let the perpendicular be x
So, perpendicular = base =x
Area of triangle =\frac{1}{2} \times base \times height
2
1
×base×height
Since we are given that the area is 100 sq.cm
So, 100=\frac{1}{2} \times x \times x100=
2
1
×x×x
200=x^2200=x
2
\sqrt{200}=x
200
=x
So, perpendicular = base = √200 cm = 10√2 cm
Now to find hypotenuse we will use Pythagoras theorem:
Hypotenuse^2=Perpendicular^2+Base^2Hypotenuse
2
=Perpendicular
2
+Base
2
Hypotenuse^2=(\sqrt{200})^2+(\sqrt{200})^2Hypotenuse
2
=(
200
)
2
+(
200
)
2
Hypotenuse^2=200+200Hypotenuse
2
=200+200
Hypotenuse^2=400Hypotenuse
2
=400
Hypotenuse=\sqrt{400}Hypotenuse=
400
Hypotenuse=20Hypotenuse=20
So, perimeter = Sum of all sides
=10\sqrt{2}+10\sqrt{2}+2010
2
+10
2
+20
=20\sqrt{2}+2020
2
+20
=48.28cm48.28cm
Hence the perimeter of triangle is 48.28 cm