Bissoy.com
Doctors Medicines MCQs Q&A

The numerical value of the area of a square is equal to half the numerical value of each of its diagonals. What is the numerical value of diagonal?

The numerical value of the area of a square is equal to half the numerical value of each of its diagonals. What is the numerical value of diagonal? Correct Answer 1

Given:

The numerical value of the area of a square is equal to half the numerical value of each of its diagonals.

Concept Used:

If the length of the sides of a square is a then the area of the square is a2 and the length of the diagonal of the square is (a√2)

Calculation:

Let, the length of the side of the square is a unit

Area of the square is a2 square unit

Length of the diagonal of the square is √2a unit

accordingly,

a2= (1/2)√2a

⇒ a2 = a/√2

⇒ a = (1/√2)

The length of the diagonal is {√2 × (1/√2) 

⇒ 1

∴ The numerical value of diagonal is 1.

Related Questions

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm
The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume of the cube is half of the numerical value of the area of the square, then the length of one side of the square is:
The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume of the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is:
The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is
The diagonal of a square A is (a + b) units. What is the area (in square units) of the square drawn on the diagonal of square B whose area is twice the area of A?
The average area of 3 square rooms I, II, and III are 1600 square meters. If one rectangular room(IV) area is added then the average area becomes 1400 square meters. If another room V, whose area is 400 square meters more than the IV room, replaces room I, then the average area of II, III, IV, and V room becomes 1350 square meters. Find the area of I room.
A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded?
The area of the square is 125/64th of the area of the rhombus. One of the diagonals of rhombus is 9 cm less than the side of square whose diagonal is 25√2 cm then find the other diagonal of the rhombus (in cm)?
Which of the following statement(s) is / are TRUE? A: Area of a kite with diagonals of length 12 cm and 15 cm is 120 cm2. B: Length of circumradius of an equilateral triangle of side 7 cm is 7√3 cm. C: Area of square whose diagonal is equal to the diagonal of a rectangle of sides 8 cm and 4 cm is 40 cm2. 
Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.