Question

what are their constribution/achievement​

Answer 1

Explanation:

Perimeter of trapezium = 104 m

Length of Non-parallel sides = 18 m and 22 m

Altitude = 16m

Area of Trapezium = 0.5 * (sum of parallel sides)*altitude ------ (1)

Sum of parallel sides = Perimeter - (sum of non-parallel sides) = 104 m - (18+22)m = 104-40 m = 64 m

From (1), Area of Trapezium = 0.5*64*16 = 512 m^2

Ans: Area of trapezium = 512 m^2

Answer 2

Explanation:

Question : Prove that√5 is irrational.

Answer :

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