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
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
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:
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 )?
Question : If the area of a square is 529 cm2, then what is the length of its diagonal?
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.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile