Question

the width of a rectangular room is 3/5 of its length x metres . If its perimeter is y metres, write an equation connecting x and y .find the floor area of the room if its perimeter is 32m

Answer 1

Given Length of the rectangular room = x.

Given breadth of the rectangular room = 3/5 * x.

                                                                  = 3x/5.

Given that perimeter = y.

We know that Perimeter of the rectangular room = 2(l + b)

                                                                          y      = 2(x + 3x/5)

                                                                          y      = 2(5x + 3x/5)

                                                                          y      = 2(8x/5)

                                                                         5y = 16x

                                                                          16x - 5y = 0


The equation connecting x and y is 16x - 5y = 0.


Given Perimeter of the floor = 32m.

32 = 2(x + 3x/5)

32 = 16x/5

160 = 16x

x = 160/15

x = 10.


Therefore Length of the rectangular room = 10m.

Therefore Breadth of the rectangular room = 3x/5

                                                                         = 3 * 10/5

                                                                         = 6m.


We know that Area of floor = length * breadth

                                              = 10 * 6

                                              = 60m.



Hope this helps!