1.  In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area calculated from these measurements?

0.6%
0.8%
0.4%
0.5%

```Answer

Answer: Option  B Explanation:Let x and y be the sides of the rectangle. then, correct area = xy.
Calculated area = (105/100 x) * (96/100 y) = 504/500 xy.
Error in measurement = (504/500 xy) - xy = 4/500 xy
Therefore  error % = { 4/500 xy * 1/xy *100}% = 4/5 % = 0.8% ```

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2.  A rectangular plot is half as long again as it is broad and its area is 2/3 hectares. Then, its length is?

33.33 m
66.66 m
100/3 m
100 m

```Answer

Answer: Option  D Explanation:Let breadth = x meters. Then, length = (3/2 x) meters.
Area = (2/3 *10000) m^2
Therefore 3/2 x * x = 2/3 * 10000 <=> x^2  = 4/9 * 10000 <=> x = 2/3 * 100
Therefore  length = 3/2 x = (3/2 * 2/3 * 100) m  =100 m. ```

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3.  A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is?

5 m
12 m
13 m
14.5 m

```Answer

Answer: Option  B Explanation:We have : lb = 60 and root of l^2+b^2 + l = 5b
Now, l^2 +b^2 = (5b - l)^2  => 24b^2 - 10lb = 0 => 24b^2 - 600 = 0
=> b^2 = 25 => b = 5.
Therefore l = (60/5) m = 12 m. So, length of the carpet = 12 m  ```

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4.  If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, Find the area of the rectangle?

130 cm^2
150 cm^2
140 cm^2
120 cm^2

```Answer

Answer: Option  D Explanation:Let length  = x and breadth  = y. Then
2 (x + y) =46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289
Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 <=> xy = 120
Therefore area = xy = 120 cm^2  ```

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5.  One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field?

120 m^2
140 m^2
160 m^2
180 m^2

```Answer

Answer: Option  A Explanation:Other side  =   (17)^2 - (15)^2   = 289 - 225   = 64   = 8 m.
Therefore area = (15 * 8) m^2 = 120 m^2 ```

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