the area of a rectangle and square is equal. and the length of the rectangle is 9 more than it breadth . if the area of rectangle is 400 cm² then find the length and breadth of the rectangle and the side of the square. ( class 8)
Answers
Step-by-step explanation:
Given:-
the area of a rectangle and square is equal. and the length of the rectangle is 9 more than it breadth . if the area of rectangle is 400 cm² .
To find:-
Find the length and breadth of the rectangle and the side of the square.
Solution:-
Let the breadth of a rectangle be X cm
Then the length = breadth +9 = X+9 cm
Area of a rectangle = length× breadth sq.units
=>(X+9)(X)=X²+9X cm²
Area of the rectangle = 400 cm²
=>X²+9X=400
=>X²+9X-400=0
=>X²-16X+25X-400=0
=>X(X-16)+25(X-16)=0
=>(X-16)(X+25)=0
=>X-16=0 or X+25=0
=>X=16 or X= -25
Since the length can not be negative
X=16
X+9=16+9=25
Length = 25 cm
Breadth =16 cm
Area of a rectangle = Area of a square
=>Area of a square = 16×25
=>Area of square =400 cm²
=>Area of a square =20² cm²
Area of a square = 20×20 cm²
Side of the square =20 cm
Answer:-
Length of the rectangle = 25 cm
Breadth of the rectangle = 16 cm
Side of the square = 20 cm
Used formulae:-
- Area of a rectangle=length×breadth sq.units
- Area of a square = side×side sq.units