the diagonal of a rectangle plot is 34cm and its perimeter is 92cm. find it's area
Answers
Answer:
Perimeter of rectangle = 92m = 2(l+b) [here l and b are length and breadth of rectangle]
l+b = 46 m
squaring both sides
l2 + b2 + 2lb = 2116
l2 + b2 = 2116 - 2lb
Diagonal = √(l2 + b2) = 34
l2 + b2 = (34)2
2116 - 2lb = 1156
lb = 480 m2
Answer:
The area of the rectangular plot is 480 cm².
Step-by-step-explanation:
We have given that,
Diagonal of a rectangular plot = 34 cm
Perimeter of rectangular plot = 92 cm
We have to find the area of the rectangular plot.
We know that,
( Diagonal )² = ( length )² + ( breadth )² - - [ Pythagors theorem ]
→ ( 34 )² = ( l )² + ( b )²
→ l² + b² = 1156 - - ( 1 )
Now, we know that,
Perimeter of rectangle = 2 ( length + breadth )
→ P = 2 ( l + b )
→ 92 = 2 ( l + b )
→ l + b = 92 ÷ 2
→ ( l + b ) = 46
→ ( l )² + 2 × l × b + ( b )² = ( 46 )² - - [ Squaring both sides ]
→ l² + 2lb + b² = 2116
→ l² + b² + 2lb = 2116
→ 1156 + 2lb = 2116 - - [ From ( 1 ) ]
→ 2lb = 2116 - 1156
→ 2lb = 960
→ lb = 960 ÷ 2
→ lb = 480 - - ( 2 )
Now, we know that,
Area of rectangle = length × breadth
→ A = l × b
→ A = 480 cm² - - [ From ( 2 ) ]
∴ The area of the rectangular plot is 480 cm².