Archives

Find two consecutive positive integers, sum of whose squares is 365.

Let us assume, the two consecutive positive integers be x and x + 1. Hence, as per the given questions, x2 + (x +... View Article

ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2 .

ΔABC is an isosceles triangle right angled at C. From ΔACB, ∠C = 90° AC = BC (By isosceles triangle property)... View Article

Solve the following equation and check your results: 2x/3 + 1 = 7x/15 + 3

Solution (2x + 3) / 3 = (7x + 45) / 15 15 (2x + 3) = 3 (7x + 45) 30x + 45 = 21x + 135 30x + 45 – 21x = 135 Rearranging... View Article

In Fig. E is any point on median AD of a ΔABC. Show that ar (ABE) = ar(ACE) .

Solution AD is median of ΔABC (Given) It divides ΔABC into two triangles of equal area. Hence, ar(ABD) = ar(ACD) ----(1)... View Article

Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9) .

Given Two points (2, – 5) and (- 2, 9) Find out We have to determine the point on the x-axis which is equidistant from (2, - 5) and (- 2,... View Article

In Fig. lines XY and MN intersect at O. If POY = 90° and a : b = 2 : 3, find c.

Given XY and MN are straight lines. ∠POY = 90° ----(i) a : b = 2 : 3 ------(ii) ∠POM = a ∠XOM = b ∠XON = c Considering XY as a straight... View Article

Find the centre of a circle passing through points (6, -6) , (3, -7) and (3, 3) .

Let us assume A = (6, -6), B = (3, -7), C = (3, 3) are the points on a circle. If O is the centre, then OA = OB = OC (radii are equal) If O = (x,... View Article

Segment of a circle is the region between an arc and _____________ of the circle.

Segment of a circle is the region between an arc and chord of the circle. A circle is a closed two-dimensional figure in which the set... View Article

Simplify and solve the following linear equation: 15(y – 4) -2(y – 9) + 5(y + 6) = 0

15(y – 4) –2(y – 9) + 5(y + 6) = 0 ⇒ 15y – 60 -2y + 18 + 5y + 30 = 0 Rearranging the equation and combining like... View Article

How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?

Given that AP. 9, 17, 25 … Find out We need to find out the number of terms for the sum 636 Solution Let there be n terms of the... View Article

ABC is a right-angled triangle in which A = 90° and AB = AC. Find ∠B and ∠C.

Solution: Given, ABC is a right-angled triangle in which ∠A = 90° and AB = AC. To find: We have to determine ∠B and ∠C Solution In right... View Article

ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that B = C.

Given: In ∆ABC, AB=BC AP ⊥ BC To Prove ∠B = ∠C. Proof In ∆APB and ∆APC ∠APB = ∠APC... View Article

Simplify and solve the following linear equation: 0.25(4f – 3) = 0.05(10f – 9)

0.25(4f – 3) = 0.05(10f – 9) => f – 0.75 = 0.5f – 0.45 Rearranging the equation and combining like terms we get... View Article

ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Let ABC is an equilateral triangle of each 2a units Construction: Draw AD ⊥ BC In right ∆ ADB (AB)2 = (AD)2 + (BD)2 (2a)2 =... View Article

Construct the following quadrilateral: Rhombus BEST. BE = 4.5 cm ET = 6 cm

Solution We know that all sides of a rhombus are of the same measure. Hence, BE = ES = ST = TB The rough sketch of the rhombus BEST can be drawn... View Article

Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term?

Given that A.P. is 3, 15, 27, 39, … Find out We need to find out the term which is 132 more than the 54th term Solution first term,... View Article

In Fig. ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF) .

Given ||gm ABCD, DCFE, and ABFE To Prove ar.(ADE)=ar.(BCF) Proof: In ∆ADE and ∆BCF AD = BC ——[opposite sides of ||gm... View Article

Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

Given: As per the given condition, x = 2 and y = 1 is solution of the equation 2x + 3y = k. On substituting the values of x and y in the... View Article

What is the minimum interior angle possible for a regular polygon? Why?

Solution An Equilateral Triangle is a regular polygon with minimum number of sides because all sides are equal in it. Each interior angle =... View Article

The sum of three consecutive multiples of 8 is 888. Find the multiples.

Solution Let the three consecutive multiples of 8 be ‘8M’, ‘8(M+1)’ Mnd ‘8(M+2)’. According to... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31