Question

of semicircle is ar
Ques. 10 Find the length of the diagonal of the rectangle whose length is equal
to 10 cm and breadth is equal to 5 cm
Ques. 11 Fill in the blanks:-​

Answer 1

Here, we are given that the length and breadth of a rectangle is 10 cm and 5 cm respectively. We have to find the length of its diagonals.

We know that measure of the angles of a rectangle is 90° each. So, we can apply pythagoras property here. According to pythagoras property, square of the longest side of right angled triangle is equivalent to the sum of square of the two remain sides.

By making a diagonal, a rectangle can be divided into two right-angled triangles. [Refer to the attachment.]

Here,

• BD is the diagonal.

In triangle BCD :

• Longest side (Hypotenuse) is BD.
• Remaining sides are DC and BC.

By using pythagoras property,

$\longrightarrow \sf {BD^2 = DC^2 + BC^2 }$

$\longrightarrow \sf {BD^2 = 10^2 + 5^2 }$

$\longrightarrow \sf {BD^2 = 100 + 25 }$

$\longrightarrow \sf {BD^2 = 125 }$

$\longrightarrow \sf {BD= \sqrt{125} }$

$\longrightarrow \sf {BD= 5 \sqrt{5} }$

$\longrightarrow\boxed{ \sf {Diagonal= 5 \sqrt{5} \: cm } }$

Therefore, diagonal of the rectangle is 5√5 cm.

More about rectangles :

• A rectangle is a quadrilateral having 4 sides, 4 angles and 4 vertices.

• Opposite sides of a rectangle are equal.

• Measure of interior angles of a rectangle is 90° each.

• Perimeter = 2(length + breadth)

• Area = Length × Breadth

Answer 2

Given :

• Length of Rectangle = 10cm
• Breadth of Rectangle = 5cm

To Find :

• Diagonal of the Rectangle

Solution :

We know that,

★ (Diagonal)² = (Length)² + (Breadth)²

⟶⠀(Diagonal)² = (Length)² + (Breadth)²

⟶⠀(AC)² = (BC)² + (AB)²

⟶⠀(AC)² = (10)² + (5)²

⟶⠀(AC)² = 100 + 25

⟶⠀(AC)² = 125

⟶⠀AC = √125

⟶⠀AC = 5cm

So, Length of the Diagonal is 5cm

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Few Properties to Learn :

Properties of rectangle are :

• Opposite sides are equal and parrallel.
• Opposite angles are equal.
• Adjacent angles are supplementary.
• Diagonals are equal.
• Each of the angles is a right angle.

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