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The length of a rectangular storage room is 2 feet longer than its width if the area of the room is 195 square feet, find its dimensions

Sagot :

oladayoademosu

The dimensions of the rectangular storage room are length = 15 ft and width = 13 ft

Let the

  • L = length of the rectangular storage room and
  • W = width of rectangular storage room.

Givent hat its length is 2 feet longer than its width, we have that

L = W + 2

Area of a rectangle

The area of the room is a rectangle A = LW where

  • L = length of room and
  • W = width of room

Since the area of the room A= 195 ft², we have that

A = LW

LW = 195

The width of the rectangular storage room

Substituting the value of L into the equation, we have

LW = 195

(W + 2)W = 195

W² + 2W = 195

W² + 2W - 195 = 0

W² + 15W - 13W - 195 = 0

W(W + 15) - 13(W + 15) = 0

(W + 15)(W - 13) = 0

W + 15 = 0 or W - 13 = 0

W = -15 or W = 13.

Since W cannot be negative, W = 13 ft

The length of the rectangular storage room

Since L = W + 2

Substituting W into the equation, we have

L = 13 + 2

L = 15 ft

So, the dimensions of the rectangular storage room are length = 15 ft and width = 13 ft

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