Question

The length and breadth of a rectangle are less than the length of its
diagonal by 1 cm and 2 cm respectively. Find the length of the diagonal
of the rectangle.
​

Answer 1

Answer:

2 cm +1 cm respectively. find the rectangle answer is 3 cm(69*) he is a answer

Answer 2

Let the length of diagonal be ‘d’.

In the given question,

• Diagonal = BD
• One side of rectangle = (d - 1)
• Other side of rectangle = (d - 2)

Since the given figure is a rectangle, ∠BCD = 90°

This forms 2 right angled triangles namely ∆BCD and ∆BAD.

Consider any 1 right angled triangle.

In ∆BCD;

By Pythagoras theorem,

(BD)² = (BC)² + (CD)²

⇒ d² = (d - 1)² + (d - 2)²

⇒ d² = d² + 1 - 2d + d² + 4 - 4d

⇒ d² = 2d² + 5 - 6d

⇒ 0 = 2d² - d² + 5 - 6d

⇒ 0 = d² - 6d + 5

⇒ d² - 6d + 5 = 0

⇒ d² - d - 5d + 5 = 0

⇒ d (d - 1) - 5 (d - 1) = 0

⇒ (d - 5) (d - 1) = 0

∴ d = 5 or 1

Case 1: If diagonal = 1 cm

Side of rectangle would be

• (d - 1) = 1 - 1 = 0 cm
• (d - 2) = 1 - 2 = -1 cm

Side cannot be negative or zero.

So, d ≠ 1

Case 2: If diagonal = 5 cm

Side of rectangle would be

• (d - 1) = 5 - 1 = 4 cm
• (d - 2) = 5 - 2 = 3 cm

These values are possible.

∴ Length of diagonal = 5 cm