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In Fig. ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC) . Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Solution Given ar(ΔDRC) = ar(ΔDPC) ar(ΔBDP) = ar(ΔARC) Prove: ABCD and DCPR are trapeziums. Proof:... View Article

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %) 45-55 55-65 65-75 75-85 85-98 Number of cities 3 10 11 8 3 Solution Class Interval Frequency (fi) (xi)... View Article

List the outcomes you can see in these experiments. (a) Spinning a wheel (b) Tossing two coins together

Solution (a) Since, there are four letters A, B, C and D in a spinning wheel Therefore there are 4 possible outcomes. (b) When two coins are... View Article

In , sides AB and AC of ΔABC are extended to points P and Q respectively. Also, PBC < QCB. Show that AC > AB.

Solution Given ∠PBC < ∠QCB To Prove PBC < QCB We know that ABC + PBC = 180° So, ABC = 180°-PBC Also, ACB +QCB = 180° Thus, ACB =... View Article

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

Volume of cube=64cm3 = (side)3 (Side)3 = 64 Side = (64cm3) 1/3 = (2*2*2*2*2*2 cm3)1/3 = 2*2 = 4 cm Hence, Length = 8... View Article

If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6) , find the values of x. Also find the distance QR and PR.

Given: Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), which means PQ = QR Let us find the distance between PQ and QR using distance... View Article

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR prove that AB/PQ = AD/PM.

Given that ΔABC ~ ΔPQR To Prove AB/PQ = AD/PM Proof We know that the corresponding sides of similar triangles are in proportion. So,... View Article

In Figure, D is a point on side BC of ∆ ABC such that BD/CD = AB/AC. Prove that AD is the bisector of ∠ BAC.

In the given figure, let us extend BA to P such that; AP = AC. Now join PC. In ΔAEC, AE=AC∠AEC=∠ACE From figure AC=AE. BDCD=ABAE... View Article

Construct the following quadrilateral: Quadrilateral GOLD. OL = 7.5 cm GL = 6 cm GD = 6 cm LD = 5 cm OD = 10 cm

Solution The rough sketch of the quadrilateral GOLD can be drawn as follows. (1) ∆ GDL can be constructed by using the given measurements as... View Article

Find the measure of ∠P and ∠S if SP || RQ ? in Fig (If you find m∠R, is there more than one method to find m∠P?)

∠P + ∠Q = 180° {angles on the same side of transversal} ⇒ ∠P + 130° = 180° ⇒ ∠P = 180° –... View Article

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Given Given that, OA = OC OB = OD and ∠AOB = ∠BOC = ∠OCD = ∠ODA = 90° AC = BD To Prove If the diagonals of a quadrilateral bisect each... View Article

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Given that S7 = 49 S17 = 289 Find out We need to find the sum of first n terms Solution We know that Sum of n terms;... View Article

The two opposite vertices of a square are (-1, 2) and (3, 2) . Find the coordinates of the other two vertices.

Let us assume ABCD is a square, where A(-1,2) and B(3,2). And Point O is the point of intersection of AC and BD To Find Coordinate of points B... View Article

Construct the following quadrilateral: Quadrilateral ABCD AB = 4.5 cm BC = 5.5 cm CD = 4 cm AD = 6 cm AC = 7 cm

Solution The rough sketch of the quadrilateral ABCD can be drawn as per the steps given below (1) ∆ABC can be constructed by using the given... View Article

Construct the following quadrilateral: Quadrilateral LIFT. LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm

Solution A rough sketch of the quadrilateral LIFT can be drawn as follows. (1) ∆ ITL can be constructed by using the given measurements as... View Article

ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig.) . Prove that (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC

Solution Given AD = BC and ∠ DAB = ∠ CBA To Prove (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC. Proof AD = BC, And ∠ DAB = ∠ CBA. On... View Article

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