Question

The length of the diagonal of a rectangle is √181 inches. ​ ​Which statement describes the length of the diagonal?

A: The length is between 12 and 13 inches.
B: The length is between 13 and 14 inches.
C: The length is between 14 and 15 inches.
D: The length is between 15 and 16 inches.

Answer 1

b

Explanation:

Answer 2

The correct option is (B).

Explanation:

The length of the diagonal of a rectangle is
`√(181)` inches.

Compute the value of
`√(181)` inches as follows:

The number 181 is not a square of a whole number.

So, the square root of 181 must lie between two whole numbers.

Consider the following squares:

`12^(2)=144`

`13^(2)=169`

`14^(2)=196`

It is quite clear that the 181 lies between the square of 13 and 14.

So, it can be said that the square root of 181 is between the square of 13 and 14.

Thus, the length of the diagonal of a rectangle is between 13 and 14 inches.

The correct option is (B).