Question

area of a rectangular feild of length 40cm is 1200sq cms . Find the area perimeter and length of diagonal of the square drawn on the diagonal of the rectangle

Answer 1

Area of the rectangle = 1200 sq cm.
length*breadth = 1200 sq cm.
40*x = 1200 sq cm. ---------------------------let breadth be x;
therefore, x = 1200 \ 40 = 30 cm. therefore the breadth of the rectangle is 30 cm.

Now by Pythagoras Theorem we find the length of the diagonal of the rectangle,
Therefore, 40² + 30² = diagonal²
              diagonal = √1600+900
              diagonal = 50 cm

Therefore the length of the side of the square is 50 cm

Now we find the area, perimeter and the length of the diagonal of the square

area of the square = side²
but side = 50 cm
therefore area of the square = 50²
                                         = 2500 sq cm

perimeter of the square = 4×50
                                  = 200 cm.

length of the diagonal ( By Pythagoras Theorem )
side² + side² = diagonal²
Therefore, diagonal =√2(2500)
                            =50√2 cm

Answer 2

length of rectangle l = 40cm
Area of rectangle (l*b) = 1200sq.cm
breadth of rectangle = 40*b = 1200
b = 1200/40 =30cm

Length of the diagonal of rectangle = √(l²+b²)
= √(40²+30²)
=√(1600+900)
=√(2500)
=50cm

Area of square = a²
side of the square a = 50cm
Area = 50² = 2500cm²

Perimeter of a square = 4a = 4*50 = 200cm

Length of the diagonal of a square = a√2 = 50√2cm