POLYNOMIAL WORD PROBLEMS INVOLVING AREA AND PERIMETER WORKSHEET

Problem 1 :

Set up an equation and hence find the value of x and find the area.

Solution

Problem 2 :

Solution

Problem 3 :

Find x given that the square and the rectangle have equal areas.

Solution

Problem 4 :

A rectangular paddock has a length 300 m greater than its width. If the perimeter of the paddock is 1400 m, find:

(a) the width (b) the length.

Solution

Problem 5 :

The length of the rectangle is 11 m more than its width, the area of the rectangle is 2040 cm². Find the dimension of the rectangle.

Solution

Problem 6 :

The perimeter of this pentagon is 70 units.

a What is the value of x?

b What is the length of the shortest side?

Solution

Problem 7 :

The isosceles triangle illustrated has a base of length 18 cm.

a) What is the value of x?

b) Is the triangle equilateral? Explain your answer.

Solution

Problem 8 :

Adjacent sides of a rhombus have lengths (2x + 11) cm and (4x + 5) cm. Find x and hence find the perimeter of the rhombus.

Answers :

(1) x = 3 and area = 36 cm².

(2) x = 7

(3) x = 3

(4) Width = 200 and length = 500.

(5) Width of the rectangle is 40, length is 51.

(6) Longest side = 24 units and shortest side = 6 units.

(7) x = 11 and it is a equilateral triangle.

(8) 68 cm.

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