Find the area of rectangle plum if entering your answer as a decimal, round your final answer to the nearest hundredth.

A = 53.34

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.

Then the length of the rectangle is 12.65

Now we solve the MALU triangle. Where MU = PL

We use the Pythagorean theorem:

Where LU and MA are unknown.

Finally we solve the triangle MPA

Where PM = LU

So:

Now we have two equations and two unknowns. So we solve the system.  (i)

 (ii)

We introduce (ii) in (i)

Now we clear MA

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

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step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺