Archives

Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2) , (-3, -5) , (3, -2) and (2, 3) .

Let the vertices of the quadrilateral be A (- 4, – 2), B ( – 3, – 5), C (3, – 2), and D (2, 3). Join AC and divide the... View Article

Find the distance between the following pairs of points: (i) (2, 3) , (4, 1) (ii) (-5, 7) , (-1, 3) (iii) (a, b) , (- a, – b)

The distance formula to find the distance between two points (x1, y1) and (x2, y2) is, say d, D = √[(x2 – x1)2 +... View Article

Construct an angle of 45° at the initial point of a given ray and justify the construction.

Procedure To construct an angle of 45°, the given steps can be followed 1. Let us draw a ray OA 2. Considering O as a centre with... View Article

Construct an angle of 90° at the initial point of a given ray and justify the construction.

Procedure To construct an angle of 90°, the given steps can be followed 1. Draw a ray OA 2. Considering O as the centre with any... View Article

Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

Given The ratio of the sides of the triangle is given as 12: 17: 25 Perimeter is 540 cm Find out We have to determine the area of a triangle... View Article

Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle

(i) a quadrilateral Solution A square is a quadrilateral, as it has four equal sides. (ii) a parallelogram Solution A square is a... View Article

The squares of which of the following would be odd numbers? i) 431 ii) 2826 iii) 7779 iv) 82004

Solution The square of an odd number will be an odd number, and the square of an even number will be an even number. i. The square of 431... View Article

Identify all the quadrilaterals that have. (a) four sides of equal length (b) four right angles

(a) four sides of equal length Solution: Rhombus and square have all sides equal. (b)four right angles Solution: Square and... View Article

In Fig, if lines PQ and RS intersect at point T, such that PRT = 40°, RPT = 95° and TSQ = 75°, find SQT.

∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75° From △PRT. ∠PRT +∠RPT + ∠PTR = 180° (The Sum of all the angles of Triangle is 180°) ⇒ ∠PTR = 45° Now... View Article

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Given AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. Find out We have to determine the area of quadrilateral Solution we can... View Article

Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6) .

Let us assume the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k :1. Therefore, -1 = (... View Article

Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

Distance between (2, – 3) and (10, y) is 10. Using distance formula, BC= √[(10 – 2)2 + (y... View Article

Find the height of the cylinder whose volume if 1.54 m² and diameter of the base is 140 cm.

Given Volume of cylinder = 1.54 m3 Diameter of cylinder = 140 cm Find out We have to find out the height of the cylinder Solution... View Article

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

Given The length of the two sides is given as 18 cm and 10 cm respectively. Perimeter = 42 cm. Find out We have to determine the area of a... View Article

In Fig. if PQ ST, PQR = 110° and RST = 130°, find QRS. [Hint : Draw a line parallel to ST through point R.]

Solution: Construct a line XY parallel to PQ. We have to find the value of ∠QRS PQ || ST [Given] and XY || ST [... View Article

If the volume of a right circular cone of height 9cm is 48πcm3, find the diameter of its base.

Given Height of cone (h) = 9 cm Volume of cone (V) = 48π cm3 Find out We have to find the diameter of its base Solution V = (1/3)... View Article

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

Solution (i) AD = BC {Opposite sides of a parallelogram are equal} (ii) ∠DCB = ∠DAB {Opposite angles of a parallelogram are... View Article

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Solution Let the present age of Ravi be ‘G’. Fifteen years later, Ravi age will be (G+15) years. Accordding to the given... View Article

Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

A number is said to be a rational number if it can be written in the form of p/q, where p and q are integers and q ≠ 0 We can write 0... View Article

In Figure, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2 BC.BD.

Given ABC is a triangle in which ∠ABC > 90∘ and AD⊥CB is produced. To Prove AC2= AB2+ BC2 – 2 BC.BD. Proof... View Article