Question

ABCD is a rhombus. AC = 40 cm and BD = 30 cm. Find DC and the perimeter of ABCD

Answer 1

Remember that

In a rhombus the diagonals are perpendicular and each diagonal bisect each other

so

triangle AEB is a right triangle

and

AE=AC/2=40/2=20 cm

EB=BD/2=30/2=15 cm

Applying the Pythagorean Theorem

AB^2=AE^2+EB^2

AB^2=20^2+15^2

AB^2=625

AB=25 cm

REmember that

the rhombus has four equal length sides

so

DC=AB=25 cm

Perimeter is

P=4(25)=100 cm