Question

If a rectangular region has perimeter P inches and area A square inches, is the region square?(1) P = 4/3*A(2) P = 4âA

Answer 1

(1) Insufficient data

(2) Sufficient data

Explanation:

We need to check whether the given data is sufficient or not to prove that a rectangular region has perimeter P inches and area A square inches, is the region square.

Assume that the given conditions are

1.
`P=(4)/(3)A`

2.
`P=4√(A)`

Area of square is

`A=a^2`

Taking square root on both sides.

`√(A)=a` .... (1)

where a is side length.

Perimeter of square is

`P=4a` ... (2)

From (1) and (2) we get

`P=4√(A)`

It means second condition is sufficient to prove that the rectangle reason is square, because it is true for all.

For a=3,

A=9 and P=12

`12=(4)/(3)(9)`

`12=12`

LHS=RHS

For a=6,

A=36 and P=24

`24=48` (False statement)

The first condition is insufficient because it may or may not be true.