Question
Note: Figure not drawn to scale.
The rectangular mirror shown above has width 3 feet and length 5 feet and is surrounded by a mosaic border with a width of x feet. If the area of the mirror with the border is 35 square feet, what is the width x, in feet, of the border?
The correct answer is: 2
Consider a rectangle with length b and width r. Then, area of the rectangle would be br sq. unit.
Explanations:
Step 1 of 3:
The rectangular mirror has width 3 feet and length 5 feet as shown in the diagram. The width of the mosaic border is x feet for both the length and breadth of the mirror.
Hence, the length and width of the mirror, along with the mosaic border, are (5 + x) feet and (3 + x) feet.
Step 2 of 3:
The area of the mirror with the border is given by 35 sq. feet.
since 20 = 10 × 2 and 10 - 2 = 8
Step 3 of 3:
The solutions of the equation (*) are given by,
Either, (x + 10) = 0
⇒x = - 10
Or, (x - 2) = 0
⇒ x = 2
The solutions of x are -10 and 2.
Since, x is a length, then it must be a positive number. Thus, x = 2 is the only solution.
Hence, the width of mosaic border (x) is 2 feet.
Final Answer:
The width x, in feet, of the border is 2.
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