ABCD IS A rectangle .find value of X and Y
DC= x+y
CB= x-y
Da=14cm
Ab=30
Answers
Answer:
x = 22 , y = 8
Step-by-step explanation:
dc = ab = 30
x + y = 30 .............(1)
bc = ad = 14
x - y = 14 ..............(2)
(1) + (2)
2x = 44
x = 22
y = 30 - 22 = 8
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Answer: 8 cm
Step-by-step explanation:
ABCD IS A rectangle .find value of X and Y DC= x+y CB= x-y Da=14cm Ab=30
Given: rectangle ABCD, DC= x+y, CB= x-y Da=14cm Ab=30
Solution:
In rectangle ABCD, AB is parallel and congruent to DC because the opposite sides of the rectangle is parallel and congruent. Therefore,
AB = DC or DC = AB
DC = AB Substitute.
x + y = 30 Equation (1)
In rectangle ABCD, CB is parallel and congruent to DA because the opposite sides of the rectangle is parallel and congruent. Therefore,
CB = DA Substitute.
x - y = 14 Equation (2)
Then, apply elimination in solving linear equations with two variables using the two equations.
x + y = 30 Equation (1)
x - y = 14 Equation (2) Add similar terms.
2x + 0 = 44
2x = 44 Divide both sides by 2 applying Division Property of Equality
2x/2 = 44/2 Applying Division Property of Equality
x = 22 cm
Substitute the value of x to any of the two equations to find the value of y.
x + y = 30 Equation (1)
22 + y = 30
22 + y + (– 22) = 30 + (– 22) Applying Addition Property of Equality by adding -22 to both sides.
22 – 22 + y = 30 – 22
0 + y = 8
y = 8 cm
Answer: The value of x is 22 cm and the value of y is 8 cm.