Question

The ratio of length and breadth of a rectangle is 4:3, if the area of the rectangle is 108 sq. cm. then find the length of its diagonal ​

Answer 1

Given: length : breadth = 4:3

           Area of given rectangle = 108sq. m

To find: length of diagonal of the rectangle.

Step by step explanation

     let the length and breadth of rectangle be 4x and 3x.

     Area of rectangle = 108 sq. m

       length ×  breadth =  108

         4x × 3x = 108

           12$x^{2}$ = 108

            $x^{2}$ = 108÷12

             x = √9

               x = 3m

       therefore, length = 4x

                                     = 4 × 3

                                      = 12m

                            breadth = 3x

                                           =3 × 3

                                            = 9 m

TO FIND THE LENGTH OF ITS  DIAGONAL : We know  that all four angles of a rectangle are 90°.

        Therefore, we can use pythagoras theorem to find the length of its diagonal .

In the given fig.

      Using pythagoras theorem,

          BD² = BC² +  DC²

          BD² = 12² + 9²

           BD² = 144 + 81

           BD² = 225

           BD = √225

            BD = 15cm

Answer: The length of diagonal is 15cm