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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