QUADRATIC EQUATIONS
Length of side of outer square = (x + 4)m
Area of the outer square = (x + 4)2
Let the length of the side of the pool be x m.
Sol.
What we need to find?
(Area of footpath)
=
(Area of pool)
2m
2m
Area of the pool
Pool is in square shape
What is area of square?
That means we need to find side of square pool
(Side)2
Area of square = (side)2
(Area of the pool) =
x2
(Area of footpath)
=
(Area of the pool)
(Area of footpath)
+
=
We have 2 things
(Area of outer square)
(Area of outer square)
For Finding Area of Outer square we will have to find the length of side of outer square
?
( ) m
x
+ 2
+ 2
+ 4
2m
2m
x m
320
32
4
8
0
Length of side of outer square = (x + 4) m
Area of the outer square = (x + 4)2
Let the length of the side of the pool be x m.
Sol.
(Area of footpath)
=
(Area of pool)
Area of square = (side)2
(Area of the pool) =
x2
(Area of footpath)
=
(Area of the pool)
(Area of footpath)
+
=
(Area of outer square)
x2
+
=
(x + 4)2
x2
=
x2 + 8x + 16
– 8x
– 16
= 0
∴ 5x
= 0
∴ (x – 8)
(5x + 8)
= 0
∴ x – 8
= 0
5x + 8
= 0
or
∴ x = 8
or
∴ x = 8
∴ x2 = 82
∴ x2 = 64
Area of pool is 64 sq.m.
Multiplying throughout by 4 we get,
5x2
∴ 5x2
= 0
Find two factors of 320 in such a way that by subtracting factors we get middle number.
–
+
– 40x
+ 8x
- 64
(x – 8)
+ 8
(x – 8)
Since last sign is ‘-’ Give middle sign to the bigger factor & opposite sign to smaller factor.
∴
‘-’ sign means subtracting
64 × 5 = 320
– 32x
– 64
= 0