Question

the perimeter of rhombus is 40 cm. if one diagonal is 16 cm find another diagonal and area

Answer 1

P=4a
a=√p2+q2/2
Solving forp
p=√1/4P^2﹣q2=1
√4·402﹣16^22=12cm
Area= 1/2×di×dii
Area =1/2×12×16
Area=1/2×192
Area=96 cm sq

Answer 2

another diagonal is 12 cm..
as you know the diagonals of a rhombos are perpendicular bisector to each other...
and the length of sides of rhombus are equal...
as perimeter is 40..
so sides will be 10cm...
and if you look the rhombus carefully you can see 4 congurent triangles and as I said the diagonals are perpendicular bisector so the two sides of each perpendicular triangle will be 10 cm and 8cm..
now we can get the third side of the triangle..
and that is 6cm...
so the length of second diagonal is 12cm...
now the area is 4*1/2*6*8=92cm^2