Question

a pair of adjacent sides of a rectangle are in the ratio 3 : 4.if its diagonal is 20cm find the length of the sides and hence the perimeter of rectangle

Answer 1

Let the length of the rectangle = 4x cm
then the breadth of the rectangle = 3x cm
Now, length of the diagonal = 20 cm⇒root[(length)²+(breadth)²] = 20⇒root[(4x)²+(3x)²] = 20
⇒root [16x²+9x² ] = 20
⇒root (25x²) = 20
⇒5x = 20
⇒x = 4
Now, length = 4x = 4×4 = 16 cm breadth = 3x = 3×4 = 12 cm
Now, perimeter = 2(length+breadth) = 2(16+12) = 2×28 = 56 cm

Answer 2

Given,

Length : Breadth = 4 : 3

Let,

Length = 4x

Breadth = 3x

Diagonal = 20 cm

Since,

Diagonal and two adjacent sides form a right angle triangle.

By Pythagorean theorem -

= (20)2 = ( 4x)2 + (3x)2

= 400 = (16x)2 + (9x)2

= 400 = (25x)2

= (x)2 = 16

=x = 4

Hence,

Length of rectangle = 4x

= 4 * 4

= 16

Breadth of rectangle = 3x

= 3 * 4

= 12

Perimeter of a rectangle = 2(Length +Breadth)

= 2 (16 +12)

= 56 cm

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