Question

Parallelogram FIRE

Given:








a. What is the value of x?
b. How long is FI?
c. What is the value of y?
d. How long is EF?
e. From your answers in b and d, what is the perimeter of parallelogram FIRE?

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Answer 1

See the solutions below

Explanation:

First note that the opposite side of a parallelogram are equal, hence;

For Parallelogram FIRE

fi = re

ef = ir

Given

fi = (3x-5)cm

ir = (2y -7)cm

re = (x+7)cm

ef = (y+3)cm\

a) If fi = re, then;

3x - 5 = x+7

3x - x = 7+5

2x = 12

x = 12/2

x = 6

b) Since FI = 3x - 5

FI = 3(6) - 5

FI = 18 - 5

FI = 13cm

c) Also ef = ir

y+3 = 2y - 7

y - 2y = -7-3

-y = -10

y = 10

d) EF = y+3

EF = 10 +3

EF =13cm

e) Perimeter of the parallelogram = FI + IR + RE + EF

Perimeter of the parallelogram = 13cm + 13 + 13cm + 13cm

Perimeter of the parallelogram = 52cm