the length of rectangle is three times of the breath if the area of the rectangle is 432 square metres then find its perimeter?
Answers
first we find length and breadth is not given .
let,the numbers be x
A/Q
Aera or rectangle = (Length * Breadth)
= 3x * x = 432
= 4x = 432
= x = 432/4 = 108
let ,we find its length and breadth
length = 108 * 3 = 324
breath = 108
then we find perimeter of rectangle
perimeter of rectangle = 2(length+breath)
= 2(324+108)
=2*432
=864
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Perimeter of rectangle is 96 cm.
Explanation:
It is given that the length of rectangle is three times of its breadth. The area of rectangle is 432 cm².
We have to find out its perimeter.
Let breadth of rectangle be y
Atq length of rectangle is three times of its breadth. So, breadth of rectangle will be 3y
Now, firstly we will find length and breadth of rectangle by using formula of area of rectangle. As we know that;
Area of rectangle = Length × Breadth
Putting all values we get,
➻ 432 = 3y × y
➻ 432 = 3y²
➻ 432/3 = y²
➻ 144 = y²
➻ y² = 144
➻ y = √(144)
➻ y = √(12 × 12)
➻ y = 12
Hence, breadth of rectangle is 12 cm.
Finding length of rectangle,
➻ Length = 3y
➻ Length = 3 × y
Put y = 12 we get,
➻ Length = 3 × 12
➻ Length = 36 cm
Hence, length of rectangle is 36 cm.
Now, we have all required things so let's calculate the perimeter of rectangle. As we know that;
Perimeter of rectangle = 2(Length + Breadth)
Putting all values we get,
➻ Perimeter = 2(36 + 12)
➻ Perimeter 2(48)
➻ Perimeter = 2 × 48
➻ Perimeter = 96 cm
Hence, perimeter of rectangle is 96 cm.
Know more:
Perimeter of any figure is calculated by sum of its all sides.
Perimeter of square = 4 × side
Area of square = (side)²
Perimeter of equilateral ∆ = 3 × side
Area of equilateral ∆ = √3/4 (side)²
Perimeter of rhombus = 4 × side
Area of rhombus = ½ × d₁ × d₂
Perimeter of circle = 2πr
Area of circle = πr²
Perimeter of rectangle = 2(l + b)
Area of rectangle = l × b
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