Question

The length of a room is three and half times its width. If the perimeter of the floor of the room is 90m, find the length and width of the room.

Answer 1

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Answer 2

Given:

Length of the room = Three and a half ($3\frac{1}{2}$) times its width.

Let the width of the room be 'b'.

Now, length of the room, l = $3\frac{1}{2}$ b

                                            = (7/2)b

Perimeter of the floor of the room, P = 90 m

Answer:

The length and width of the room are 35 m and 10 m respectively.

Find:

The length and width of the room.

Solution:

The floor of the room is in the shape of a rectangle.

∴ Perimeter of the floor, P = 2(l + b)

where l = length of the room

b = width of the room

But Perimeter, P = 90

Perimeter of the floor = 2(l + b)

90 = 2(l + b)

90/2 = l + b

But l = (7/2) b

Now, we have

45 = (7/2)b + b

45 = (7b + 2b)/2

45 = 9b/2

45 × 2 = 9b

9b = 45 × 2

9b = 90

b = 90/9

b = 10 m

Hence, width of the room, b = 10 m.

Length of the room, l = (7/2) × b

                                   = (7/2) × 10

                                   = 7 × 5 m = 35 m

Hence, length of the room, l = 35 m.

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