PROPERTIES OF RECTANGLES WORKSHEET

Find the values of unknown.

Problem 1 :

Solution

Problem 2 :

Find the values of x and y.

Solution

Problem 3 :

Find the value of x.

Solution

Problem 4 :

In a given figure, ABCD is a rectangle and its diagonals meet at O. Find x, if OA = 2x + 4 and OD = 3x + 1. Also find BD.

Solution

Problem 5 :

The measure of the diagonal of a rectangle is 5 cm. If one of its sides is 3 cm, then find its perimeter.

Solution

Problem 6 :

ABCD is a rectangle and diagonals intersect at O. If ∠AOB = 118. Find

(i)  ∠ABO    (ii)  ∠ADO      (iii)  ∠OCB

Solution

Problem 7 :

What is the area and length of the diagonal of a rectangle with adjacent side lengths of 24 cm and 7 cm?

Solution

Problem 8 :

The diagonal of a rectangle has a length of 100 cm, and its length is twice its width. Find the area of this triangle.

Solution

Problem 9 :

Find

(i)  SQ  (ii)  PR   (iii)  QR   (iv)  SR

Solution

Problem 10 :

Find

(i)  ∠MJK   (ii)  ∠MJL   (iii)  ∠KML     (iv)  ∠MNL

Problem 11 :

Find

(i)  AD   (ii)  BD  (iii)  BC  (iv)  BE

Solution

Problem 12 :

In the given rectangle, find ∠1 and ∠2.

Problem 13 :

Find x.

Problem 14 :

In the rectangle given below, find the value of x.

Problem 15 :

In the rectangle given below, the length of the diagonal is 36. Find values of x and y.

Problem 16 :

In rectangle ABCD, AC = x + 8, AB = x + 7 and AD = x. Find the value of x, also find AC, AB and AD.

Solution

1)  x = 2.5 cm

2)  x = 40 and y = 100

3)  x = 65

4)  BD = 20

5)  Missing side = 4 cm, perimeter = 12 cm

6)  ∠OBA = 31, ∠ADB = 59

∠OCB = 59

7)  Diagonal = 25

8) 4000 cm2

9)  SQ = 26, RP = 26 ,OQ = 10, SR = 24

10)  (i)  ∠MJK = 90, (ii)  ∠MJL = 63

(iii)  ∠KML = 27 (iv)  ∠MNL = 126

11)  (i)  AD = √171  (ii)  BD = 30

(iii)  BC = √171    (iv)  BE = 15

12)  x = 14, ∠PMQ = 42 and ∠QPM = 48

13) x = 14 cm

14)  x = 3

15)  x = 5 and y = 2

16)  AB = 12, AC = 13 and AD = 5.

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