Question

Rhombus LMNO is shown with its diagonals.

The length of LN is 28 centimeters. What is the length of LP?
A.7 cm
B.9 cm
C.14 cm
D.21 cm

Answer 1

the diagonals cut each other in two
so LP = 1/2 * 28 = 14

C

Answer 2

we know that

Rhombus diagonals are perpendicular bisectors of each other

so

`LN=LP+PN\\LP=PN`

so

`LN=2LP`

Solve for LP

`LP=(1)/(2) LN`

we have

`LN=28\ cm`

substitute

`LP=(1)/(2)*28=14\ cm`

therefore

the answer is the option C

`LP=14\ cm`