in the given figure abcd is a rectangle find the value of x and y
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In Fig. 1, ABCD is a rectangle. Find the values of x and y .
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In Fig. 1,ABCD is a rectangle. Find the values of x and y.
∵ ABCD is a rectangle, the length of opposites sides are equal.Easy Open in App Solution Verified by Toppr ⇒AB=CDandAD=BC x+y=30 ...... (1) x−y=14 ..... (2)
Adding (1)+(2)⇒2x=44⇒x=
2 44 =22 cm.
Subtracting (1)−(2)⇒2y=16⇒y=
2 16 =8 cm. ∴x=22 cmandy=8 cm.
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In fig. 1, ABCD is a rectangle. Find the values of x and y.
In fig. 1, ABCD is a rectangle. Find the values of x and y.
Byju's Answer Standard X Mathematics
Multiplying/Dividing a Negative Entity
In fig. 1, AB... Question
In fig. 1, ABCD is a rectangle. Find the values of x and y.
Open in App Solution
Given, ABCD is a rectangle.
∴ AB = CD ⇒ 30 = x + y
or x + y = 30 ..... (i)
Similarly, AD = BC ⇒ 14 = x - y
or x - y = 14 .......(ii)
On adding eq. (i) and (ii), we get
2x = 44 ⇒ x = 22
Putting the value of x in eq. (i), we get
22 + y = 30 ⇒ y = 30 -22 ⇒ y = 8 So, x = 22, y = 8. Suggest Corrections 62
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Prev Question 13 Next
In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.
(i)
Answer:
(i) From the figure we know that the diagonals are equal and bisect at point O.
Consider △ AOB We get AO = OB
We know that the base angles are equal
∠ OAB = ∠ OBA = 35
By using the sum property of triangle
∠ AOB + ∠ OAB + ∠ OBA = 180
By substituting the values we get
∠ AOB + 35+ 35 = 180
On further calculation
∠ AOB = 180 - 35 - 35
By subtraction ∠ AOB = 180 - 70 ∠ AOB = 110
From the figure we know that the vertically opposite angles are equal
∠ DOC = ∠ AOB = y = 110
In △ ABC
We know that ∠ ABC = 90
Consider △ OBC We know that
∠ OBC = x = ∠ ABC - ∠ OBA
By substituting the values
∠ OBC = 90 - 35 By subtraction ∠ OBC = 55
Therefore, x = 55 and y = 110.
(ii) From the figure we know that the diagonals of a rectangle are equal and bisect each other.
Consider △ AOB We get OA = OB
We know that the base angles are equal
∠ OAB = ∠ OBA
By using the sum property of triangle
∠ AOB + ∠ OAB + ∠ OBA = 180
By substituting the values
110 + ∠ OAB + ∠ OBA = 180
We know that ∠ OAB = ∠ OBA
So we get 2 ∠ OAB = 180 - 110 By subtraction 2 ∠ OAB = 70 By division ∠ OAB = 35
We know that AB || CD and AC is a transversal
From the figure we know that ∠ DCA and ∠ CAB are alternate angles
∠ DCA = ∠ CAB = y = 35
Consider △ ABC We know that ∠ ACB + ∠ CAB = 90 So we get ∠ ACB = 90 - ∠ CAB
By substituting the values in above equation
∠ ACB = 90 - 35 By subtraction ∠ ACB = x = 55
Therefore, x = 55 and y = 35.
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