Set up an equation and hence find the value of x :
Problem 1 :
Solution :
Perimeter of rectangle = 2 (l + w)
Let l and w be the length and width of the rectangle
Here, l = 3x - 5 and
w = x + 1
Perimeter of rectangle = 24 m
2 (l + w) = 24
2(3x - 5 + x + 1) = 24
6x – 10 + 2x + 2 = 24
8x – 8 = 24
8x = 24 + 8
8x = 32
x = 32/8
x = 4
The value of x is 4.
Problem 2 :
Solution :
Perimeter of triangle = a + b + c
Let a, b and c be the sides of the triangle respectively.
Perimeter = 15 m
Sum of all sides = 15
x – 2 + x – 2 + x + 1 = 15
2 (x – 2) + (x + 1) = 15
2x – 4 + x + 1 = 15
3x – 3 = 15
3x = 15 + 3
3x = 18
x = 18/3
x = 6
The value of x is 6.
Problem 3 :
Solution :
Using exterior angles theorem,
x + (2x + 10) = (4x – 22)
x + 2x + 10 = 4x - 22
3x + 10 = 4x - 22
10 + 22 = 4x - 3
32 = x
The value of x is 32.
Find the perimeter of the rectangle. Your answer must not contain x.
Problem 4 :
Solution :
Perimeter of rectangle = 2 (l + w)
Let l and w be the length and width of the rectangle
Here, l = (3x - 4) cm and (x + 14) cm and
w = (x + 6) cm
(3x - 4) = (x + 14)
3x – x = 14 + 4
2x = 18
x = 9
(3x – 4) is the length of the rectangle.
l = 3x – 4
l = 3(9) – 4
l = 27 – 4
l = 23
(x + 6) is the width of the rectangle.
w = x + 6
w = 9 + 6
w = 15
Perimeter of rectangle = 2 (l + w)
= 2 (23 + 15)
= 2(38)
= 76
The Perimeter of rectangle = 76 cm
Set an equation and hence find the value of x.
Problem 5 :
Solution :
The Sum of interior angles of a quadrilateral is 360º.
90 + 4x + 5 + 3x + 10 + 3x + 5 = 360
110 + 10x = 360
10x = 360 – 110
10x = 250
x = 250/10
x = 25
The value of x = 25
Problem 6 :
Solution :
Perimeter of rectangle = 2 (l + w)
Let l and w be the length and width of the rectangle
Here , l = 2x + 2 cm and
w = 4x - 1 cm
perimeter of rectangle = 62 cm
2 (l + w) = 62
2 (2x + 2 + 4x -1) = 62
2(6x + 1) = 62
12x + 2 = 62
12x = 62 – 2
12x = 60
x = 60/12
x = 5
The value of x is 5.
Problem 7 :
Solution :
x + x + x – 5 + x – 5 + x + 3 = 53
5x – 7 = 53
5x = 53 + 7
5x = 60
x = 60/5
x = 12
The value of x is 12.
Problem 8 :
Find x if the square and triangle have the same area :
Solution :
area of square = area of triangle
a2 = 1/2 h b
(x + 2)2 = 1/2 (x + 5) · 2x
x2 + 4 + 4 x = (x + 5) · x
x2 + 4 + 4 x = x2 + 5x
x2 + 4 + 4x – x2 – 5x
4 – x
x = 4
Problem 9 :
Find x if both rectangles are having the same area :
Solution :
Area of rectangles = l x w
(x + 5) x (x – 2) = (x + 3) x (x – 1)
x2 – 2x + 5x – 10 = x2 – x + 3x - 3
x2 + 3x – 10 = x2 + 2x – 3
x2 + 3x – 10 - x2 - 2x + 3 = 0
x – 7 = 0
x = 7
Two rectangles have the same area.
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