Question

If the given rectangle is an equable shape, then the value of y is

a) 1.1 centimeters

b) 10 centimeters

c) 2.5 centimeters

d) 4.5 centimeters​

Answer 1

• Addition: Kindly check the attachment for the rectangle.
• Equable rectangle: an equable rectangle has its perimeter and area numerically equivalent.

Solution:

Given that, x cm and y cm are length and width respectively of the rectangle.

Then its

• perimeter = 2 (x + y) cm
• area = xy sq. cm

Given, x = 10 cm

Since the given rectangle is equable, we write:

2 (x + y) = xy

or, 2 (10 + y) = 10y

or, 10 + y = 5y

or, 5y - y = 10

or, 4y = 10

or, 2y = 5

or, y = 2.5

Therefore, the value of y is 2.5 cm.

Option (c) 2.5 centimetres.

Answer 2

The value of y is c) 2.5 centimetres.

Step-by-step explanation:

The image given in the question is attached below.

The perimeter of a rectangle is given by the formula:

P = 2(x + y)

The area of a rectangle is given by the formula:

A = xy

Now, from questions the rectangle is equable. Thus,

Perimeter = Area

2(x + y) = xy

On substituting the value of 'x', we get,

2(10 + y) = 10y

20 + 2y = 10y

20 = 8y

y = 20/8

∴ y = 2.5 cm