Question

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

Answer 1

Answer:

$P = 22.75$

Step-by-step 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

$\frac{NT}{3.9} = \frac{6.5}{5.2}$

Make NT, the subject:

$NT = \frac{6.5}{5.2}*3.9$

$NT = \frac{6.5*3.9}{5.2}$

$NT = \frac{25.35}{5.2}$

$NT = 4.875$

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