Question

the area of a rectangle of length 20cm and diagonal 29 is​

Answer 1

Answer:

Area of rectangle is 420cm².

Step-by-step explanation:

Given:

• Length and Diagonal of a rectangle are 20cm and 29cm respectively.

To find:

• We need to find the area of rectangle.

Solution:

Please refer the attachment for better understanding.

To find the area of rectangle, we need to know the values of length and breadth. Since, we don't know the value of breadth, we are going to find it first by using Pythagoras Theorem.

As you can see the attached figure, let us assume:

• Length = AB
• Diagonal = AC
• Breadth = BC

Here,

• Length acts as base.
• Diagonal acts as Hypotenuse.
• Breadth acts as Perpendicular side.

Accirding to Pythagoras Theorem,

$\star\;\underline{\boxed{\sf{\pink{(Hypotenuse)^2 =\ \bf (Perpendicular)^2+(Base)²}}}}$

On applying the formula, we get:

$\sf{\longrightarrow (AC)^2 = (BC)^2+(AB)^2}$

$\sf{\longrightarrow (29)^2 = (BC)^2+(20)^2}$

$\sf{\longrightarrow 841 = (BC)^2+400}$

$\sf{\longrightarrow (BC)^2 = 841 - 400}$

$\sf{\longrightarrow (BC)^2 = 441}$

$\sf{\longrightarrow BC = \sqrt{441}}$

$\longrightarrow {\underline{\boxed{ \sf{ \orange{BC\ = 21\ cm}}}}}\ \bigstar$

Hence, the breadth of rectangle is 21 cm.

Formula to find area of rectangle:

$\star\;\underline{\boxed{\sf{\purple{Area = Length \times Breadth}}}}$

On applying the formula, we get:

$\sf{\longrightarrow Area = Length \times Breadth}$

$\sf{\longrightarrow Area = 20 \times 21}$

$\longrightarrow {\underline{\boxed{ \sf{ \red{Area = 420\:cm^2}}}}}\ \bigstar$

Hence, the area of rectangle is 420cm².

Answer 2

Given :

• Length of Rectangle = 20cm
• Diagonal of Rectangle = 29cm

To Find :

• Area of Rectangle

Solution :

Finding the breadth first :

We know that,

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

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

⠀⟶⠀(BD)² = (BC)² + (DC)²

⠀⟶⠀(29)² = (20)² + (DC)²

⠀⟶⠀841 = 400 + (DC)²

⠀⟶⠀841 - 400 = (DC)²

⠀⟶⠀441 = (DC)²

⠀⟶⠀√441 = DC

⠀⟶⠀21cm = DC⠀⠀⠀⠀⠀[Breadth]

Finding the Area of Rectangle :

We know that,

★ Area of Rectangle = Length × Breadth

⟶ Area of Rectangle = Length × Breadth

⟶ Area of Rectangle = 20 × 21

⟶ Area of Rectangle = 420cm²

So, Area of Rectangle is 420cm²

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