111k views
0 votes
Given: LMNK is a rhombus

KM + LN = 7
Area of KLMN = 6.

Find: KL

1 Answer

6 votes
we know that
The area of a rhombus is half the product of the diagonals
so
A=(1/2)*[KM*LN]
A=6 units²
6=(1/2)*[KM*LN]-----> 12=KM*LN-----> KM=12/LN-----> equation 1
KM+LN=7-----> equation 2

substitute equation 1 in equation 2
[12/LN]+LN=7------> multiply by LN both sides----> 12+LN²=7LN
LN²-7LN+12=0

using a graph tool
see the attached figure
LN=3
KM=4

find KL
applying the Pythagoras Theorem
KL²=(LN/2)²+(KM/2)²-----> (3/2)²+(4/2)²----> 25/4
KL=5/2-----> KL=2.5 units

the answer is
KL=2.5 units
Given: LMNK is a rhombus KM + LN = 7 Area of KLMN = 6. Find: KL-example-1
User Moxy
by
7.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.