Answer:
[tex]P = 22.75[/tex]
Step-by-step explanation:
Given:
See attachment for rectangle LINT
Required
Calculate its perimeter
From the attachment:
Considering triangle LYT, we apply Pythagoras theorem.
[tex]LT^2 = LY^2 + TY^2[/tex]
Where:
[tex]LY = 5.2[/tex]
[tex]TY = 3.9[/tex]
The formula becomes:
[tex]LT^2 = 5.2^2 + 3.9^2[/tex]
[tex]LT^2 = 42.25[/tex]
Take positive square root of both sides
[tex]LT = \sqrt{42.25[/tex]
[tex]LT = 6.5[/tex]
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
[tex]NT:TY = LT:LY[/tex]
[tex]NT : 3.9 = 6.5 : 5.2[/tex]
Convert to fractions
[tex]\frac{NT}{3.9} = \frac{6.5}{5.2}[/tex]
Make NT, the subject:
[tex]NT = \frac{6.5}{5.2}*3.9[/tex]
[tex]NT = \frac{6.5*3.9}{5.2}[/tex]
[tex]NT = \frac{25.35}{5.2}[/tex]
[tex]NT = 4.875[/tex]
The perimeter (P) is then calculated as:
[tex]P = NT + LT + LI + NI[/tex]
Where
[tex]NT = LI[/tex] and [tex]LT = NI[/tex] -- opposite sides of rectangle.
So:
[tex]P = NT + NT + LT + LT[/tex]
[tex]P = 2NT + 2LT[/tex]
Substitute values for NT and LT
[tex]P = 2*4.875 + 2*6.5[/tex]
[tex]P = 9.75 + 13.0[/tex]
[tex]P = 22.75[/tex]
Hence, the perimeter is 22.75 units
