Question

Consider rectangle, square, triangle and circle as 4 given shapes with a common area of 314 sq.Cm. The length of a rectangle is 2cm and height of right-angled triangle is 4cm. Find the shape which has the smallest perimeter and largest perimeter in c++

Answer 1

Answer:

Triangle has Maximum Perimeter and Circle has Minimum Perimeter.

Step-by-step explanation:

Given: Area of a Rectangle = Area of Square = Area of Right angled traingle

           = Area of circle = 314 cm²

          Length of rectangle = 2 cm, Height of Traingle = 4 cm.

To find: Shape which has smallest perimeter and lasregest perimeter.

1). Length of rectangle = 2 cm

Area of Rectangle = 314 cm²

Length × Breadth = 314

2 × breadth = 314

breadth = $\frac{314}{2}$

Breadth = 157 cm

⇒ Perimeter of Rectangle = 2 × ( Length + Breadth )

                                           = 2 × ( 2 + 157 )

                                           = 2 × ( 159 )

  Perimeter of Rectangle = 318 cm

2). Height of Right angled triangle = 4 cm

Area of Right angled Triangle = 314 cm ²

$\frac{1}{2}\times Base \times Height=314$

$\frac{1}{2}\times Base \times 4=314$

$Base \times 2=314$

$Base=\frac{314}{2}$

Base = 157 cm

For Perimeter We first find 3rd side, by pythagoras theorem

(Hypotenous)² = (Base)² + (Height)²

(Hypotenous)² = 4² + 157²

(Hypotenous)² = 16 + 24649

(Hypotenous)² = 24665

Hypotenous = √24665

Hypotenous = 157.05 cm

⇒ Perimeter of Triangle = 4 + 157.05 + 157

  Perimeter of Triangle  = 318.51 cm

3).

Area of Square = 314 cm²

(Side)² = 314

Side = √314

Side = 17.72 cm

Perimeter of square = 4 × Side

                                 = 4 × 17.72

Perimeter of square = 70.88 cm

4).

Area of Circle = 314 cm²

$\pi r^2=314$

$r^2=\frac{314}{3.14}$

$r^2=100$

$r=\sqrt{100}$

r = 10 cm

Circumference of Circle = $2\pi r$

                                        = $2\times3.14\times10$

Circumference of Circle = 62.8 cm

Therefore, Triangle has Maximum Perimeter and Circle has Minimum Perimeter

Answer 2

Answer:

Answer:

Triangle has Maximum Perimeter and Circle has Minimum Perimeter.

Step-by-step explanation:

 

Given: Area of a Rectangle = Area of Square = Area of Right angled traingle

          = Area of circle = 314 cm²

         Length of rectangle = 2 cm, Height of Traingle = 4 cm.

To find: Shape which has smallest perimeter and lasregest perimeter.

1). Length of rectangle = 2 cm

Area of Rectangle = 314 cm²

Length × Breadth = 314

2 × breadth = 314

breadth =  

Breadth = 157 cm

⇒ Perimeter of Rectangle = 2 × ( Length + Breadth )

                                          = 2 × ( 2 + 157 )

                                          = 2 × ( 159 )

 Perimeter of Rectangle = 318 cm

2). Height of Right angled triangle = 4 cm

Area of Right angled Triangle = 314 cm ²

Base = 157 cm

For Perimeter We first find 3rd side, by pythagoras theorem

(Hypotenous)² = (Base)² + (Height)²

(Hypotenous)² = 4² + 157²

(Hypotenous)² = 16 + 24649

(Hypotenous)² = 24665

Hypotenous = √24665

Hypotenous = 157.05 cm

⇒ Perimeter of Triangle = 4 + 157.05 + 157

 Perimeter of Triangle  = 318.51 cm

3).

Area of Square = 314 cm²

(Side)² = 314

Side = √314

Side = 17.72 cm

Perimeter of square = 4 × Side

                                = 4 × 17.72

Perimeter of square = 70.88 cm

4).

Area of Circle = 314 cm²

r = 10 cm

Circumference of Circle =  

                                       =  

Circumference of Circle = 62.8 cm

Therefore, Triangle has Maximum Perimeter and Circle has Minimum Perimeter