Question

can any one help plz

Answer 1

for part a :
find the area of square
find the area of triangle

add them both

Answer 2

area of square = (4x-4)^2

Answer 3

area of triangle = 1/2 (4x-4)(2x-2)

Answer 4

Area of pentagon = (4x-4)^2 + 1/2(4x-4)(2x-2)

Answer 5

simplify

Answer 6

ok..why do we add the 1/2

Answer 7

good question :)

Answer 8

maybe first factor out 4

Answer 9

\((4x-4)^2 + \frac{1}{2}(4x-4)(2x-2)\)

\(4^2(x-1)^2 + \frac{1}{2}4(x-1)2(x-1)\)

\(16(x-1)^2 + 4(x-1)(x-1)\)

\(16(x-1)^2 + 4(x-1)^2\)

\(20(x-1)^2 \)

Answer 10

thats the final simplified expression

Answer 11

see if that looks okay

Answer 12

next, think about part b

Answer 13

oh thanks now i knew why 1/2

Answer 14

good :)

Answer 15

we start multiplying the answer and see if we get the expression

Answer 16

@ganeshie8

Answer 17

area of triangle = 1/2 (4x-4)(2x-2)
hi sorry but how did u to this for the triangle ?

Answer 18

area of triangle = 1/2(b)(h)

Answer 19

isn't the answer have to be
(16+4) (x-1)

Answer 20

@ganeshie8

Answer 21

how ?

Answer 22

we're done wid part a right ?

Answer 23

by grouping

Answer 24

it shoudl be (16+4)(x-1)^2 okay ?

Answer 25

when u add u wud get :

20(x-1)^2

Answer 26

thats for part a

Answer 27

oh ok...

Answer 28

ya now part be we will be checking how is it the right answer

Answer 29

b

Answer 30

for part b, u may do below :-

plugin x = 2,
and see wat u get for area using the simplified formula : 20(x-1)^2

Answer 31

next,
when x = 2, find out area of square and triangle separately. and add them.

Answer 32

u should get the same answer by using both mehtods..

Answer 33

Area of pentagon using simplified formula, when x = 2 :-

A = 20(2-1)^2 = 20

Answer 34

why =20

Answer 35

Area of square = (4*2-4)(4*2-4) = (4)(4) = 16

Area of triangle = 1/2(4*2-4)(2*2-2) = 1/2(4)(2) = 4

adding them gives : 16+4 = 20

so we just verified that the formula is correct for x = 2

Answer 36

how did u solve for square

Answer 37

Area of square = (4x-4)(4x-4)

Answer 38

plugin x = 2 above

Answer 39

4(2)-4 4(2)-4

Answer 40

then here how do we get 16

Answer 41

whats 4(2) - 4 ?

Answer 42

4

Answer 43

yes

Answer 44

then 4*4 =16

Answer 45

yup

Answer 46

then with the triangle im confused in solving it

Answer 47

write down Area of triangle formula first

Answer 48

1/2(4*2-4)(2*2-2)

Answer 49

Area of triangle = 1/2(4x-4)(2x-2)

Answer 50

plugin x = 2

Answer 51

1/2 4(2)-4 2 (2)-2

Answer 52

@ganeshie8

Answer 53

yes, simplify it

Answer 54

1/2 [4(2)-4 ] [2 (2)-2]

Answer 55

4 +2

Answer 56

nope,

1/2 [4(2)-4 ] [2 (2)-2]


first u need to work the thing inside parenthesis

Answer 57

1/2 [4(2)-4 ] [2 (2)-2]
^^^^^ ^^^^^

Answer 58

oh ok

Answer 59

1/2[8 - 4] [4 - 2]

Answer 60

1/2[4] [2]

Answer 61

4

Answer 62

ohh ok

Answer 63

lets do c

Answer 64

@ganeshie8

Answer 65

for part c,
start by writing out the area of triangle formula again

Answer 66

Area of triangle = \(\large \frac{1}{2}(4x-4)(2x-2)\)

Answer 67

right ?

Answer 68

yes

Answer 69

\(\large \frac{1}{2}(4x-4)(2x-2)\)

\(\large \frac{1}{2}4(x-1)2(x-1)\)

\(\large 4(x-1)^2\)

Answer 70

right ?

Answer 71

yes

Answer 72

\(\large 4(x-1)^2\)

take 4 inside the square, it becoems :

\(\large (2(x-1))^2\)

\(\large (2x-2)^2\)

Answer 73

clearly thats the area of a square of side (2x-2)

Answer 74

so, for part c, the required area of square is : \(\large (2x-2)^2\)

Answer 75

then d

Answer 76

expand the square

Answer 77

u knw below identity

(a + b)^2 = a^2 + 2ab + b^2

right ?

Answer 78

use it

Answer 79

\((2x-2)^2 = ?\)

Answer 80

yes

Answer 81

(2x+2)(2x-2)

Answer 82

?

Answer 83

nope, use the identity...

Answer 84

\((2x-2)^2 = (2x)^2 - 2(2x)(2) + 2^2\)

Answer 85

\( = 4x^2 - 8x + 4\)

Answer 86

what type of polynomial it is ?

Answer 87

what is it?

Answer 88

how many terms it has

Answer 89

?

Answer 90

\(4x^2-8x+4\)

Answer 91

3 terms right ?

Answer 92

so its called a "trinomial"

Answer 93

i really didnt understand how did u expand that

Answer 94

do u knw below formula ?

\((a+b)^2 = a^2 + 2ab + b^2\)

Answer 95

yes

Answer 96

oh k