Q. 3

# We have seen in Class 7 that any odd number can be written as the difference of two perfect squares. (The lesson, **Identities**) Usingthis, draw lines of lengths centimetres.

Answer :

→ Any odd number can be written in the form 2k – 1,k being a natural number.

Now,2k – 1 = k^{2} – (k – 1)^{2}

● For,

2k – 1 = 7

⇒2k = 8

⇒ k = 4

So, √7 = 4^{2} – 3^{2}

So, if we draw a line of 4 units, say CD, then,

Then,

Draw a random line and cut a length of 3c.m. s off it, to have AB.

→ Then draw a normal BA’ on AB.

→ Draw a circular arc with A as the centre and CD as centre, which eventually intersects BA’ at E.

→ Join B and E; and, A and E.

See, In Δ ABE, –

AB⊥ BE

BE^{2} = AE^{2} – AB^{2} = 4^{2} – 3^{2} = 7

⇔ E = √7 c.m.

● And,

2k – 1 = 11

⇒ 2k = 12

⇒ k = 6

So, √11 = √( 6^{2} – 5^{2})

Draw a random line and cut a length of 5 c.m. s off it, to have AB.

→ Then draw a normal BA’ on AB.

→ Draw a circular arc with A as the centre and CD as centre, which eventually intersects BA’ at E.

→ Join B and E; and,A and E.

See, In Δ ABE, –

AB⊥ BE

BE^{2} = AE^{2} – AB^{2} = 6^{2} – 5^{2} = 11

óBE = √11 c.m.

Rate this question :

We have seen in Class 7 that any odd number can be written as the difference of two perfect squares. (The lesson, **Identities**) Usingthis, draw lines of lengths centimetres.

The picture shows a tan gram of 7 pieces made by cutting a square of side 4 centimetres. Calculate the length of the sides of each piece.

Kerala Board Mathematics Part-1

Prove that Can you find other numbers like this?

Kerala Board Mathematics Part-1Prove that Use this to compute correct to two decimal places.

Kerala Board Mathematics Part-1Compute correct to two decimal places.

Kerala Board Mathematics Part-1The picture shows the vertices of a regular hexagon connected by lines.

i) Prove that the inner red hexagon is also regular.

ii) How much of a side of the large hexagon is a side of the small hexagon?

iii) How much of the area of the large hexagon is the area of the small hexagon?

Kerala Board Mathematics Part-1The hypotenuse of a right triangle is metres and another side is metre. Calculate its perimeter correct to a centimetre.

Kerala Board Mathematics Part-1The picture shows an equilateral triangle cut into halves by a line through vertex.

i) What is the perimeter of a part?

ii) How much less than the perimeter of the whole triangle is this?

Kerala Board Mathematics Part-1Calculate the length of the sides of the equilateral triangle on the right, correct to a millimetre.

Kerala Board Mathematics Part-1

Explain two different methods of drawing a line of length centimetres.

Kerala Board Mathematics Part-1