Question

Find the area of rectangle PLUM

Answer 1

Answer:

A = 53.34 $units ^ 2$

Step-by-step explanation:

To find the length of the rectangle we solve the PLA triangle

Using the Pythagorean theorem we find the PL side.

$PL = \sqrt{4^2+12^2}\\PL = \sqrt{16+144}\\PL = 12.65$

Then the length of the rectangle is 12.65

Now we solve the MALU triangle. Where MU = PL

We use the Pythagorean theorem:

$MU^2+LU^2 = (MA + AL)^2\\12.65^2+LU^2 = (MA+12)^2$

Where LU and MA are unknown.

Finally we solve the triangle MPA

$MA^2 + PA^2 = PM ^2$

Where PM = LU

So:

$MA^2 + 4^2 = LU^2$

Now we have two equations and two unknowns. So we solve the system.$12.65^2 + LU^2 = (MA + 12) ^2$  (i)

$MA^2+4^2 = LU^2$  (ii)

We introduce (ii) in (i)

$12.65^2 + MA^2+16=MA^2+24MA+144$

Now we clear MA

$160.02+16-1 44 = 24MA$

$32.02 = 24MA$

$MA = \frac{32.02}{24}$

MA = 1.3342 (iii)

Now we introduce (iii) in (ii)

1.3342^2 + 4^2 = LU^2

LU = 4.2166

Now we have the length of the rectangle and also its width.

The area A of a rectangle is:

A = l*w

Where

 l = length

w = width

A = 4.2166*12.65

A = 53.34 $units^2$