Question

The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.

Answer 1

Perimeter of Parallelogram ABCD: Pp=10 cm
BD=?
Perimeter of triangle ABD: Pt=8 cm

Parallelogram ABCD:
AB=CD=L1
BC=AD=L2
Pp=2(L1+L2)
10 cm=2(L1+L2)
Dividing by 2 both sides of the equation:
(10 cm)/2=2(L1+L2)/2
5 cm=L1+L2
L1+L2=5 cm

Triangle ABD
Pt=AB+BD+AD
8 cm=L1+BD+L2
8 cm=BD+L1+L2
But L1+L2=5 cm, then:
8 cm=BD+5 cm
Solving for BD:
8 cm-5 cm=BD+5 cm+ 5 cm
3 cm=BD
BD=3 cm

Answer: The length of the diagonal BD is 3 cm