28 28. Assertion (A) : V-1xV-2=-V2 Reason (R) : Vax Vb = Jab, a, bER a) Both A and R correct and R is the correct explanation of A b) Both A and R correct but R is not the correct explanation of A ) A is correct and R is incorrect d) A is incorrect and R is correct A
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Answers
Answer:
Given: Rectangular Area = 300 sq. m. = L x W
Perimeter = 70 m = 2 L + 2 W
Find: length and width
Either formula can be used with the other formula to help.
From P => (70 - 2W)/2 = L
Now substitute into the area formula.
300 = [(70 - 2W)/2] x W simply and solve
300 = (35 - W) x W Therefore
300 = 35W - W^2. Or
W^2 - 35W + 300 = 0
(W - 20)(W - 15) = 0 =>
W - 20 = 0 or W - 15 = 0 Therefore: W = 20 or W = 15
If W = 20 L = (70 - 2(20))/2 = (70 - 40)/2 = 30/2 = 15
If W = 15 L = (70 - 2(15))/2 = (70 - 30)/2 = 40/2 = 20
Solutions: Width = 20 m, Length = 15 m or
vice versa Width = 15 m, Length = 20 m
You can easily check:
A = L x W = 15 m x 20 m = 300 m^2 = 20 m x 15 m
P = 2L + 2W = 2(15m) + 2(20m) = 70 m = 2(20m) + 2(15m)
Double Check
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Sudhakar Babu DS, Puzzle Enthusiast
Answered October 14, 2020 · Author has 149 answers and 581.2K answer views
The diagonal of a rectangle field is 16 meter more than the shorter side. If the longer side is 14 meters more than shorter side, then what is the length of the side of the field?
Let a and b be the longer and shorter sides of the rectangular field
Then the diagonal is square root of (a^2 + b^2)
As the diagonal is 16 m more than the shorter side
We have (a^2 + b^2) = (b + 16)^2
On simplification, a^2 - 32b - 256 = 0 ---> Eq.1
We also have b = a - 14
On substituting above value of b in Eq.1, we get
a^2 - 32a + 192 = 0
(a - 8)(a - 24) =0
One of the above factors evaluates to 0
Obviously (a - 24) should be zero as the longer side can not be 8 m
Therefore a = 24 m and b = 24-14 = 10 m (and the diagonal is 26 m)
Longer side is 24 m and the shorter side is 10 m