A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is 7 8 that of the lawn, find the dimensions of the lawn.

Let us assume the side of the square lawn be x m. Area of the square lawn = x 2 m 2 The square lawn is bounded on three sides by a path which is 4 m wide. Area of outer rectangle = ( x + 4 ) ( x + 8 ) = x 2 + 12 x + 32 Area of path = x 2 + 12 x + 32 - x 2 = 12 x + 32 From the given information, we have: 12 x + 32 = 7 8 x 2 96 x + 256 = 7 x 2 7 x 2 - 96 x - 256 = 0 7 x 2 - 112 x + 16 x - 256 = 0 7 x ( x - 16 ) + 16 ( x - 16 ) = 0 ( x - 16 ) ( 7 x + 16 ) = 0 ( x - 16 ) = 0 Or ( 7 x + 16 ) = 0 x = 16 Or x = - 16 7 Since, x cannot be negative. So, x = 16 m . Thus, each side of the square lawn is 16 m .

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A footpath of uniform width runs round the inside of a rectangular field $32 m$ long and $24 m$ wide. If the path occupies $208 m^{2}$ , find the width of the footpath.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 8

Two squares have sides

x c m

and

(x + 4) c m .

. The sum of their areas is

656 sq . cm

. Express this as an algebraic equation in

x

and solve the equation to find the sides of the squares.

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10th ICSE

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Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 9

The dimensions of a rectangular field are

50 m

40 m

. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and graveling the path at

₹ 30

and

₹ 20

per square metre, respectively, is

₹ 52, 000

. Find the width of the gravel path.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 10

An area is paved with square tiles of a certain size and the number required is

128

. If the tiles had been

2 cm

smaller each way,

200

tiles would have been needed to pave the same area. Find the size of the larger tiles.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 11

A farmer has

70 m

of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is

600 sq . m

, find the length of its shorter side.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 12

A square lawn is bounded on three sides by a path

4 m

wide. If the area of the path is

\frac{7}{8}

that of the lawn, find the dimensions of the lawn.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 13

The area of a big rectangular room is

300 m^{2}

. If the length were decreased by

5 m

and the breadth increased by

5 m

; the area would be unaltered. Find the length of the room.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 1

The speed of an ordinary train is $x km per hr$ and that of an express train is $(x + 25) km per hr$ .

Find the time taken by each train to cover $300 km$ .

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 1

The speed of an ordinary train is $x km per hr$ and that of an express train is $(x + 25) km per hr$ . If the ordinary train takes $2 hrs$ more than the express train to cover a distance of $300 km$ , calculate speed of the express train.

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m2, find the width of the footpath.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

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A footpath of uniform width runs round the inside of a rectangular field $32 m$ long and $24 m$ wide. If the path occupies $208 m^{2}$ , find the width of the footpath.