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 1 :

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

Solution

Problem 2 :

Find x.

Solution

Problem 3 :

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

Solution

Problem 4 :

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

Solution

Problem 5 :

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

Solution

Problem 6 :

In rectangle QRST, QS = 5x − 31 and RT = 2x + 11. Find the lengths of the diagonals of QRST.

Solution

Problem 7 :

the diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure.

Solution

Problem 8 :

complete each statement with always, sometimes, or never. Explain your reasoning.

a)  A rectangle is _________ a square.

b) A rectangle _________ has congruent diagonals.

c)  A rectangle _________ has perpendicular diagonals.

Solution

Problem 9 :

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

Solution

Problem 1 :

PRST is a rectangle, find each angle if m∠1 = 50°

Solution

PRST is a rectangle, find the value of each variable.

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

PS = 6x + 3, RT = 7x - 2

Solution

Problem 5 :

Solution

Problem 6 :

ABCD is a rectangle, with diagonals that intersect at E. Find the value of each variable

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

AC = x + 7, DB = 6x - 8

Solution

Problem 10 :

In the diagram below, ABCD is a rectangle with diagonals AC and BD . If the m∠2 = 58, find the measures of angles 1, 3, and 4.

Solution

Problem 11 :

ABCD is a rectangle with diagonals AC and BD. If AC = 6x + 2 and DB = 12x – 10, find the value of x.

Solution