Question

the adjacent sides of a rectangle are 7cm and 24cm. Find the length of its diagonal​

Answer 1

Answer:

In a rectangle, all the angles are equal to 90

∘

.

On applying Pythagoras theorem in Δ ABD,

AB

2

+AD

2

=DB

2

⇒24

2

+7

2

=DB

2

⇒576+49=DB

2

⇒DB

2

=625

⇒DB=25cm

Thus, the length of the diagonal is 25cm.

Answer 2

Solution -

We have,

• Breadth of a rectangle = 7cm
• Length of a rectangle = 24cm

⠀

Now,

• Let AC be the required diagonal of the rectangle.

We know that, each angle of a rectangle is of 90°. Therefore, we apply pythagoras theorem

⠀

According to Pythagoras theorem

• In a right angled triangle, square of hypotenuse is equal to the sum of squares of other two sides.

⠀

In right angled ∆ABC

⠀⠀⠀⠀★ AC² = AB² + BC²

⠀

⇢ AC² = (7)² + (24)²

⇢ AC² = 49 + 576

⇢ AC² = 625

⇢ AC = √625

⇢ AC = 25

⠀

Hence,

• Diagonal of the rectangle is 25cm.

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