Area of rectangle :
Here we are going to see how to find the area of any rectangle. Here we give clear explanation about rectangle.
A plane figure with four straight sides and four right angles.In which the opposite sides are having the same length.
Formula:
Area of rectangle = L x B
Here "L" represents length of the rectangle and "B" represents the breadth of the rectangle.
Problem 1:
Find the area of the rectangle whose length is 15 cm and breadth is 20 cm.
Solution :
Area of a rectangle = L x B
Here length (l) = 15 cm and breadth = 20 cm
= 15 x 20
= 300 cm²
Problem 2 :
Find the area of the rectangle having the diagonal is measuring 13 cm and
length measuring 12 cm.
Solution :
The diagonal divides the rectangle into two right triangle. In the right triangle ABC the right angled at B.
The side which is opposite to 90°degree is called hypotenuse side. By using Pythagorean theorem
AC² = AB² + BC²
13² = 12² + BC²
169 = 144 + BC²
169 - 144 = BC²
25 = BC²
BC = √25
BC = √5 x 5
BC = 5
So, breadth of the rectangle = 5 cm
Area of the rectangle = Length x Breadth
= 12 x 5
= 60 cm²
Problem 3 :
The
length and breadth of the rectangle are in the ratio 5:2 .If the area
of the rectangle is measuring 147 cm². Then find the length and breadth
of the rectangle.
Solution :
5x and 2x be the length and breadth of the rectangle respectively.
Area of the rectangle = 147 cm²
Length x breadth = 147
5x x 2x = 147
7x² = 147
x² = 147/7
x² = 21
x = √21
Length = 5x = 5√21 cm
Breadth = 2x = 2√21 cm
Problem 4 :
Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of $12.40 per square meter.
Solution :
From the given information we come to know that
Area of carpet = Area of room ---- (1)
area of rectangle = length x breadth
0.75 x breadth of carpet = 13 x 9
breadth of carpet = (13 x 9) /0.75
= 117/0.75
= 156 m
Cost of carpeting = 156 x 12.40 = $ 1934.40
Problem 5:
If the diagonal of a rectangle is 17 cm long its perimeter is 46 cm, find the area of rectangle.
Solution :
Let "x" and "y" be the length and breadth of the rectangle respectively.
perimeter of rectangle = 46
2 (x + y) = 46
y = 23 - x -----(1)
x² + y² = 17²
x² + y² = 289 -----(2)
Substitute (1) in the second equation
x² + (23- x)² = 289
x² + (23)² + x² - 2 (23)(x) = 289
2x² - 46x + 529 - 289 = 0
2x² - 46 x + 240 = 0
divide the whole equation by 2
x² - 23 x + 120 = 0
(x - 15) (x - 8) = 0
x = 15 x = 8
y = 23 - 15 y = 23 - 8
y = 8 y = 15
So, length of rectangle = 15 m and
breadth of rectangle= 8 m
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