Question

A rectangular mirror 10 cm long and 8 cm wide is surrounded by a frame of uniform width x cm. Obtain an expression in terms of x for the area of the frame is 88 sq.cm . Find x

Answer 1

Step-by-step explanation:

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Answer 2

The width of the frame surrounded the rectangular mirror is 2 cm

Given : Length of rectangular mirror = 10 cm

            Width of rectangular mirror = 8 cm

          Area of the frame surrounded the rectangular mirror = 88 $cm^{2}$

To Find : Width of the frame surrounded the mirror

Solution : The width of the frame surrounded the rectangular mirror is 2 cm

It is given that the length of the rectangle is 10 cm ,

                            width of the rectangle is 8 cm

                  area of the frame surrounded the rectangular mirror is 88 $cm^{2}$

Let the rectangular mirror is surrounded by a frame of uniform width x cm.

When the rectangular mirror is surrounded by a frame of uniform width x cm then the frame is divided into four rectangles and four squares

Each square is of side x cm

So area of each square is side × side is  $x^{2}$ $cm^{2}$

Area of four squares is 4 $x^{2}$  $cm^{2}$

Two rectangles has length 8 cm and breadth x cm

Area of this rectangle is length × breadth is 8x  $cm^{2}$

Two rectangles has length 10 cm and breadth x cm

Area of this rectangle is  10x  $cm^{2}$

The sum of the area of four squares and four rectangles gives the area of the frame

So adding area of all the four rectangles and all four squares we have

  4 $x^{2}$  + 2(8x) + 2(10x) = 88

=  4 $x^{2}$ + 16x+20x = 88

= 4 $x^{2}$  +36x - 88 = 0

=  $x^{2}$ + 9x - 22 = 0

Solving the following quadratic equation we get

($-9$ ± $\sqrt{81-4(1)(-22)}$ ) / 2

=( $-9$ ± $\sqrt{169}$ ) / 2

= $\frac{-9 +13}{2}$   and $\frac{-9 - 13}{2}$

$\frac{4}{2}$   and $\frac{-22}{2}$

2 and -11

Since distance can never be negative so -11 is not possible

So the width of the frame is 2 cm

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