31.2k views
5 votes
In the given figure, ABCD is a rectangle. Its diagonals meet at O. If OC = 3x – 4, OB = x + 4, then find OB, OC, OA, AC, BD and OD​

In the given figure, ABCD is a rectangle. Its diagonals meet at O. If OC = 3x – 4, OB-example-1
User JSprang
by
8.5k points

1 Answer

3 votes

Answer:

OB = 8

OC = 8

OA = 8

AC = 16

BD = 16

OD = 8

Explanation:

Given, rectangle ABCD, with diagonals AC and BD, and OC = 3x – 4, OB = x + 4,

thus, since diagonals of a rectangle are equal, therefore, AC = BD.

Invariably, 2*OC = 2*OB

Thus,
2(3x - 4) = 2(x + 4)

Solve for x


6x - 8 = 2x + 8

Add 8 to both sides


6x - 8 + 8 = 2x + 8 + 8


6x = 2x + 16

Subtract 2x from both sides


6x - 2x = 2x + 16 - 2x


4x = 16

Divide both sides by 4


(4x)/(4) = (16)/(4)


x = 4

OB = x + 4 = 4 + 4 = 8

OC = 3x - 4 = 3(4) - 4 = 12 - 4 = 8

OA = OC = 8

AC = 2*OC = 2*8 = 16

BD = 2*OB = 2*8 = 16

OD = OB = 8

User Borowis
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories