the side of a square grassy plot is 75 m. Two cross paths each 5 m wide are constructed at right angles through the centre of the plot such that each path is parallel to the side of the plot. Determine the area of the paths
Answers
Step-by-step explanation:
Perimeter of trapezium = 104 m
Length of Non-parallel sides = 18 m and 22 m
Altitude = 16m
Area of Trapezium = ½ × (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 m²
Ans: Area of trapezium = 512 m²
Step-by-step 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