Solve (iii) question given in the image.

Answers
Answer:
Step-by-step explanation:
Lets assume side of one square to be a. Let the other side be b.
Lets also assume that a>b.
a^2 + b^2 = 400
4a - 4b = 16
Now express RHS as a product of squares.
a^2 + b^2 = 4 * 100
4a - 4b = 16
4a = 16 + 4b
Now divide by 4.
a = 4 + b
b = a-4
Now put in the values.
a^2 + b^2 = 400
(4+b)^2 + b^2 = 400
16 + b^2 + 8b + b^2 = 400
16 + 8b + 2b^2 = 400
Now divide by 2
8 + 4b + b^2 = 200
b^2 + 4b + 8 = 200
Now solve the quadratic equation.
b^2 + 4b + 8 - 200 = 0
b^2 + 4b - 192 = 0
Use is the quadratic formula. Here, a b and c refer to the terms in the standard form (ax^2 + bx + c).
Now put in the values.
x = -b ± (b^2 - 4ac)^1/2
--------------------------------
2a
a = 1
b = 4
c = -192
x = -4 ± (16 - -768)^1/2
--------------------------
2a
x = -4 ± (784)^1/2
-------------------
2
x = -4 + 28
----------
2
x = 24/2
x = 12
Therefore, the side is 12m.
(We could have done -4 - 28/2 but then we would have gotten a negative answer, and since a square cant have a side length that's negative we dont consider it.)
- Sum of areas of two squares = 400sq m
- Difference between perimeter = 16 m
- Sides of the square
- Let the side of first square be x m
- And the side of second square be y m
According to the question,
Again,
Substituting the value of x from (i)
Now factorizing :
Since the side can't be negative we take y as 12 .
Substituting the value of y in (i)
So side of first square is 16 m and that of second is 12 m .
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- Thnku ❣