Question : The height of a trapezium is 68 cm, and the sum of its parallel sides is 75 cm. If the area of the trapezium is $\frac{6}{17}$ times of the area of a square, then the length of the diagonal of the square is: (Take $\sqrt{2}=1.41$ )
Option 1: 127.39 cm
Option 2: 183.49 cm
Option 3: 119.85 cm
Option 4: 102.39 cm
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Correct Answer: 119.85 cm
Solution : Given, The height of a trapezium is 68 cm, the sum of its parallel sides is 75 cm and the area of the trapezium is $\frac{6}{17}$ times the area of a square. Area of the trapezium = $\frac{(a+b)h}{2}$, where $(a+b)$ is the sum of its parallel sides and $h$ is height. Area of the square = $a^2$, where $a$ is the length of each side. Diagonal of a square = $\sqrt2a$ So, the area of the trapezium = $\frac{68×75}{2} = 2550$ According to the question, The area of the trapezium = $\frac{6}{17}$ × the area of a square ⇒ 2550 = $\frac{6}{17}$ × the area of a square ⇒ Area of the square = $\frac{17}{6}×2550=a^2$ ⇒ $a=\sqrt{7225}$ ⇒ $a=85$ cm ⇒ The length of the diagonal of the square is $1.41×85=119.85$ cm Hence, the correct answer is 119.85 cm.
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Question : The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 cm$^2$ the sum of the length of the parallel sides is:
Option 1: 15 cm
Option 2: 36 cm
Option 3: 42 cm
Option 4: 60 cm
Question : The ratio of the length of parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. If the area of the trapezium is 450 cm2, the sum of the length of parallel sides is:
Question : The lengths of the parallel sides of a trapezium are $x$ cm and $y$ cm and the area of the trapezium is $\frac{1}{2}\left(x^2-y^2\right) cm^2$. What is the distance between the parallel sides (in cm )?
Option 1: $x$ - $y$
Option 2: $x$ + $y$
Option 3: $y$
Option 4: $x$
Question : If the area of a square is 529 cm2, then what is the length of its diagonal?
Option 1: $23\mathrm{~cm}$
Option 2: $26 \sqrt{3} \mathrm{~cm}$
Option 3: $23 \sqrt{2 } \mathrm{~cm}$
Option 4: $46 \mathrm{~cm}$
Question : Find the area of the trapezium whose parallel sides measure 14 cm, and 18 cm and the distance between parallel sides is 15 cm.
Option 1: 310 cm2
Option 2: 300 cm2
Option 3: 220 cm2
Option 4: 240 cm2
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