Question

The length and width of a rectangle are in the ratio 4:3 .If the diagonal measures 24 cm . find the length and width of the rectangle

Answer 1

Answer :

• Length of rectangle = 19.2 cm
• Breadth of rectangle = 14.4 cm

Given :

• The length and width of a rectangle are in the ratio 4:3 .
• The diagonal measures 24 cm.

To Find :

• Length of rectangle = ?
• Breadth of rectangle = ?

Solution :

• Perimeter = 24 cm

• Let Length of rectangle be 4x and breadth of rectangle be 3x

$\bigstar\:\:\displaystyle \underline{\textsf{According to Question now :}}$

$:\implies \sf Diagonal = \sqrt{(Length)^2 + (Breadth)^2}$

$:\implies \sf 24 = \sqrt{(4x)^2 + (3x)^2}$

$:\implies \sf 24 = \sqrt{16x^{2} + 9x^{2} }$

$:\implies \sf 24 = \sqrt{25x^{2} }$

$:\implies \sf 24 = 5x$

$:\implies \sf x = \frac{24}{5}$

$:\implies \underline{ \boxed{\sf x = 4.8 \:cm}}$

$\bigstar\:\:\displaystyle \underline{\textsf{Dimensions of rectangle :}}$

$\bullet\:\:\textsf{Length of rectangle = 4x = 4(4.8) = \textbf{19.2 cm}}.$

$\bullet\:\:\textsf{Breadth of rectangle = 3x = 3(4.8) = \textbf{14.4 cm}}.$

Answer 2

Question :-

The length and width of a rectangle are in the ratio 4:3 .If the diagonal measures 24 cm . find the length and width of the rectangle.

Answer :-

Length ↠19.2 cm

Breadth of rectangle ↠ 14.4 cm

Given : -

The ratio of length and breadth ↠ 4:3 .

Diagonal ↠ 24 cm.

Have to Find :-

What's the measurements of Length and breadth ?

$\Large{\underline{\underline{\bf{Calculations:-}}}}$

From the given , we consider

Length ↠ 4x

Breadth ↠ 3x

Perimeter = 24 cm

As we know The diagonal = √ length² + breadth²

24 = √ 4x² + 3x²

24 = √ 16x² + 9x²

24 = √ 25x²

Now , removing root we get ,

24 = 5x

x = 24/5

x = 4.8cm

Now ,we got " x "

Substituting the value of x

• Breadth = 3x

= 3 × (4.8)

= 14.4 cm

• Length = 4x

= 4 × (4.8)

= 19.2 cm