Question

If entering your answer as a decimal, round your final answer to the nearest hundredth.

Find the perimeter of rectangle LINT.
​

Answer 1

`P = 22.75`

Explanation:

Given:

See attachment for rectangle LINT

Required

Calculate its perimeter

From the attachment:

Considering triangle LYT, we apply Pythagoras theorem.

`LT^2 = LY^2 + TY^2`

Where:

`LY = 5.2`

`TY = 3.9`

The formula becomes:

`LT^2 = 5.2^2 + 3.9^2`

`LT^2 = 42.25`

Take positive square root of both sides

`LT = \sqrt{42.25`

`LT = 6.5`

Next, we calculate the length of NT.

By comparing triangles LYT and NYT

We make use of the following equivalent ratios to solve for NT

`NT:TY = LT:LY`

`NT : 3.9 = 6.5 : 5.2`

Convert to fractions

`(NT)/(3.9) = (6.5)/(5.2)`

Make NT, the subject:

`NT = (6.5)/(5.2)*3.9`

`NT = (6.5*3.9)/(5.2)`

`NT = (25.35)/(5.2)`

`NT = 4.875`

The perimeter (P) is then calculated as:

`P = NT + LT + LI + NI`

Where

`NT = LI` and
`LT = NI` -- opposite sides of rectangle.

So:

`P = NT + NT + LT + LT`

`P = 2NT + 2LT`

Substitute values for NT and LT

`P = 2*4.875 + 2*6.5`

`P = 9.75 + 13.0`

`P = 22.75`

Hence, the perimeter is 22.75 units