Question

Find the distance between the following pairs of points:

(2,3) (4,1)

(d) Find the area of triangle whose vertices are

(2,3) (-1,0) ( 2,-4)

(e) Find the triangle ABC ,right triangle at B , AB = 24cm BC =

7cm . Determine

Sin A , cos A

(f) Prove that √5 is irrational number.​

Answer 1

Answer:

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Answer 2

Answer:

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Step-by-step explanation:

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4. Let us assume that √5 is a rational number.

Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0

⇒√5=p/q

On squaring both the sides we get,

⇒5=p²/q²

⇒5q²=p² —————–(i)

p²/5= q²

So 5 divides p

p is a multiple of 5

⇒p=5m

⇒p²=25m² ————-(ii)

From equations (i) and (ii), we get,

5q²=25m²

⇒q²=5m²

⇒q² is a multiple of 5

⇒q is a multiple of 5

Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√5 is an irrational number

Hence proved

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