Question

The diagonal of a rectangular field is 169m. If the ratio of the length to the width is 12:5 find (¡) the dimensions (¡¡) perimeter of the field

Answer 1

The dimensions are 156m and 65 m

The perimeter of the field is 442 m.

What is Perimeter of rectangle?

The perimeter of the rectangle is the product of length to its breadth.

i.e., Perimeter= 2( l + b)

As, the diagonal of every rectangle makes right angled triangle with respect of length and width.

Diagonal² = length² + width²

Let the common ration be x

then, length = 12x and breadth = 5x

Diagonal² = length² + width²

                = (12x)²+ (5x)²

                 = 144 x² + 25 x²

                 = 169 x²

169² = 169 x²

x²= 169

x= 13

Hence, length = 12x = 12 * 13 = 156 m

width = 5x = 5*13 = 65 m

(ii) Perimeter,

= 2 ( l+ b)

= 2 ( 156 + 65 )

=2( 221)

= 442 m

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