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.
Area of rectangle = L x B
Here "L" represents length of the rectangle and "B" represents the breadth of the rectangle.
Find the area of the rectangle whose length is 15 cm and breadth is 20 cm.
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.
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 :
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.
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.
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
= 156 m
Cost of carpeting = 156 x 12.40 = $ 1934.40
If the diagonal of a rectangle is 17 cm long its perimeter is 46 cm, find the area of rectangle.
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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