Answer:
KL = 13 cm
Step-by-step explanation:
Given:
Perimeter of quadrilateral JKLM = 90 cm
KL = n
KJ = n + 7
LM = 2n - 12
MJ = 3n + 4
Required:
Length of side KL
SOLUTION:
[tex] KL + kJ + LM + MJ = [/tex] Perimeter of quadrilateral JKLM
[tex] n + (n + 7) + (2n - 12) + (3n + 4) = 90 [/tex] (substitution)
Solve for n
[tex] n + n + 7 + 2n - 12 + 3n + 4 = 90 [/tex]
Combine like terms
[tex] n + n + 2n + 3n + 7 - 12 + 4 = 90 [/tex]
[tex] 7n - 1 = 90 [/tex]
Add 1 to both sides
[tex] 7n - 1 + 1 = 90 + 1 [/tex]
[tex] 7n = 91 [/tex]
Divide both sides by 7
[tex] \frac{7n}{7} = \frac{91}{7} [/tex]
[tex] n = 13 [/tex]
KL = n = 13 cm
