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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

Suppose you are given a circle. Give a construction to find its centre.

Given below are the steps to determine the centre of the circle Step I: At first draw a circle Step II: Two chords AB and CD are to... View Article

Draw the graph of the following linear equations in two variables: y = 3x

To draw the graph y=3x, we have to find the values which x and y can have, satisfying the equation. We can check that when, x = 0, y = -2, When x... View Article

Write a Pythagorean triplet whose one member is. i) 6 ii) 14 iii) 16 iv) 18

Solution For any natural number m, we know that 2m, m2 – 1, m2 + 1 is a Pythagorean triplet. (i) 6 2m = 6 m = 6/2 = 3 m2 – 1= 32 – 1 = 9 –... View Article

Construct the following quadrilateral: Rhombus BEND. BN = 5.6 cm DE = 6.5 cm

Solution We know that the diagonals of a rhombus always bisect each other at 90º. Let us predict that these are intersecting each... View Article

What do we call the gravitational force between the earth and an object?

The gravitational force between the earth and an object is known as the object’s weight. Weight is the measure of the force of gravity... View Article

Show that in a right-angled triangle, the hypotenuse is the longest side.

Solution Given Right angle triangle intersect ∠B=90° To Prove AC>AB and AC>BC Solution ∠A+∠B+∠C=180° —————-[angle sum property]... View Article

Draw the graph of the following linear equations in two variables: x-y = 2

To draw the graph x–y = 2, we have to find the values which x and y can have, satisfying the equation. We can check that when, x = 0, y =... View Article

Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]

Given Radius of hemisphere, r = 10cm Find out We have to find the total surface area of hemisphere Formula: Total surface area of hemisphere =... View Article

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