Question

What is the area of each of the two right angled triangles Formed by the diagonal of a rectangle having area 100 sq.units? Why?​

Answer 1

Answer:

Let length of the other perpendicular side be a cm and altitude on the hypotenuse is p cm.

⇒

2

1

×4×a=20

⇒a=10 cm

∴ Hypotenuse =

a

2

+4

2

=

10

2

+4

2

=2

29

Area of the triangle =

2

1

×2

29

×p=20 sq. cm

∴p=

29

20

Answer 2

Therefore the area of each of the 2 right-angled triangles formed by the diagonal of a rectangle is 50 units².

Given:

The area of the rectangle = A = 100 units²

To Find:

The area of each of the 2 right-angled triangles formed by the diagonal of a rectangle.

Solution:

The given question can be solved as shown below.

Let the length of the rectangle = a units

Let the breadth of the rectangle = b units

→ Then in the right-angled triangle,

The base of the triangle = length of the rectangle = a units

The height of the triangle = breadth of the rectangle = b units

The hypotenuse of the triangle = diagonal of the rectangle

⇒ Area of the rectangle = length × breadth = ab = 100 units²

⇒ Area of the triangle = (1/2 ) base × height = (1/2) ab = (1/2) × 100 = 50 units²

Therefore the area of each of the 2 right-angled triangles formed by the diagonal of a rectangle is 50 units².

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