Question

If the length of rectangles having perimeter 50 centimetres is taken as x and its area as a(x),then

a. Write the relationship between x and a(x) as an equation.

b.Find a(10) and a(15)

​

Answer 1

Step-by-step explanation:

Perimeter = 2 (l + b) = 50cm

l + b = 50cm/2

= 25cm

So, x + b = 25cm

or. b = 25cm - x

Area. = l * b

or a(x) = x(25 - x)

a(10) = 10cm(25cm - 10cm)

= 10 cm * 15 cm

= 150cm2

a(15) = 15cm(25 - 15cm)

= 15cm * 10cm

= 150cm2

Answer 2

a. The relationship between x and a(x) : a(x) = x(25 - x)

b. a(10) = 150 , a(15) = 150

Given :

The length of rectangles having perimeter 50 centimetres is taken as x and its area as a(x)

To find :

a. Write the relationship between x and a(x) as an equation.

b. Find a(10) and a(15)

Solution :

Step 1 of 3 :

Express breadth of the rectangle in terms of x

Length of the rectangle = x

Perimeter = 50 centimetres

∴ 2 × (Length + Breadth) = 50

⇒ 2 × (x + Breadth) = 50

⇒ x + Breadth = 25

⇒ Breadth = 25 - x

Step 2 of 3 :

Find the relationship between x and a(x)

a(x)

= Area of the rectangle

= Length × Breadth

= x(25 - x)

∴ a(x) = x(25 - x)

Step 3 of 3 :

Find the value of a(10) and a(15)

a(x) = x(25 - x)

Putting x = 10 we get

a(10) = 10(25 - 10) = 10 × 15 = 150

a(x) = x(25 - x)

Putting x = 15 we get

a(15) = 15(25 - 15) = 15 × 10 = 150

∴ a(10) = 150 , a(15) = 150

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