Q 14....is the question....A man _______rectangular plot.
Answers
GIVEN :-
- length of a rectangular plot is (4x + 3) units
- breadth of a rectangular plot is (2x - 3) units
- side of first square shaped room is (x + 1) units
- side of second square shaped room is (x - 1) units.
TO FIND :-
- Area of remaining part of the rectangular plot .
SOLUTION :-
☞ Area of rectangle = length × breadth
⇛(4x + 3) (2x - 3) unit²
⇛4x(2x - 3) + 3(2x - 3)
⇛8x² - 12x + 6x - 9
⇛8x² - 6x - 9
☞ Area of 1st square = (side)²
⇛(x + 1)²
⇛x² + 2x + 1
☞ Area of 2nd square = (side)²
⇛(x - 1)²
⇛x² - 2x + 1
☞ Area of Remaining part = Area(rectangle) - Area of both square
⇛[(8x² - 6x - 9 ) - (x² + 2x + 1 + x² - 2x + 1)]
⇛[(8x² - 6x - 9) - (2x² + 2)]
⇛8x² - 2x² - 6x - 9 - 2
⇛6x² - 6x - 11
Hence the area of the remaining part is 6x² - 6x -11
Answer:
Length = ( 4x + 3 ) units
Breadth = ( 2x - 3 ) units
Area of plot = length × breadth
= ( 4x + 3 ) ( 2x - 3 )
= 4x ( 2x - 3 ) + 3 ( 2x - 3 )
= 8x² - 12x + 6x - 9
= 8x² - 6x - 9 ............ (1)
Side of 1st Square = ( x + 1 ) units
Side of 2nd Square = ( x - 1 ) units
Area of Both Square = ( Side )² + ( side )²
= ( x + 1 )² + ( x + 1 )²
= x² + 2x + 1² + x² - 2x + 1²
= 2x² + 1 + 1
= 2x² + 2 ...................(2)
Area of Remaining part = (1) - (2)
= ( 8x² - 6x - 9 ) - ( 2x² + 2 )
= 8x² - 6x - 9 - 2x² - 2
= 8x² - 2x² - 6x -9 - 2
= 6x² - 6x -11
.°. Area of Remaining part = 6x² - 6x - 11 ...