Solve the following mathematics problems:

The perimeter of a square is equal to the perimeter of rectangle. The length of the rectangle is three times longer than its width having total area of 1,200 sq meters. What will be the total cost if the total area of the square is covered is covered with stones having a dimension of 50 centimeter square each and if Tk. 50 is charged for placing as stone in the square?

Created: 3 months ago | Updated: 3 months ago

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Let, width of the rectangle be x meter

Length of the rectangle be 3x meter

According to question,

$3 x \times x = 1, 200 \Rightarrow 3 x^{2} = 1, 200 \Rightarrow x^{2} = \frac{1, 200}{3} x^{2} = 400 ∴ x = \sqrt{400} x = \sqrt{{(20)}^{2}} x = 20$

The perimeter of rectangle will be $2 [(3 \times 20) + 20] = 2 (60 + 20) = 2 \times 80 = 160$ meter

Perimeter of the square, 4a=160

One side of the square will be 40 meter

Area of the square will be = (40 x 40) = 1,600m²

Now, length of 1 stone is 50cm = $\frac{50}{100} = 0.5 m$

Area of one stone will be = $(0.5 x 0.5) = 0.25 m ²$

Number of stone required to cover the square = 1,600+0.25=6,400 pieces

Total amount of taka required at 50 tk per stone is $6, 400 \times 50 = 3, 20, 000$ Tk. ans.

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simplify: $\frac{5 x + 2}{x^{2} - x - 20} + \frac{2 x - 1}{x^{2} - 4 x - 5}$

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Solve the following mathematical problems:

In a survey at an airport, 55 travelers said that last year they had been to Spain, 53 to Fr and 79 to Germany, 18 had been to Spain and France, 17 to Spain and Germany and 2 France and Germany, while 10 had to all three countries. How many travelers took part survey?

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Solve the following mathematical problems:

A shopkeeper sells two shirts at the same price. He makes 10% profit on one and loses 10 the other. How much in percentage does he gain or lose?

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Solve the following mathematical problems:

The length of a tangent from a point A at distance 5cm from the center of the circle is 4cm. Find the radius of the circle

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Solve the following mathematical problems:

Find the H.C.F. of $x^{3} - 16 x, 2 x^{2} + 9 x^{2} + 4 x, 2 x^{3} + x^{3} - 28 x$

Created: 3 months ago | Updated: 3 months ago

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