Question

Rectangle STUV has square PQRS removed, leaving an area of 92 m^2. Side PT is 4 m in length and side RV is 8m in length

Answer 1

Answer:

117 $m^{2}$

Step-by-step explanation:

First think of the square that was removed.  All 4 sides are equal but you don't know the length so lets gives them the variable X.

So to find the area of the rectangle, insert those variables into the area equation for a rectangle.

(RV + (X) ) (PT +(X)) = rectangle area

Now you are given what the area is if you remove the square.  So subtract the the square's area from the equation above and set it equal to the size they told you.

(RV + (X)) (PT + (X))  - [(X)(X)] = 92$m^{2}$

      rectangle          -  square  =  remaining area

Now plug in the numbers you know and solve for X.

(8 + X) (4 + X) - ((X)(X)) = 92    

Use FOIL to multiply the first part of the equation (first, outer, inner, last)

32 + 8x + 4x + $x^{2}$ -  $x^{2}$  =  92

32 + 12x = 92

12x = 60

x = 5

So now you know the size of the square.  Each side is 5m.  So add 5m onto the top of the rectangle and onto the side.  The top is 13m and the side is 9m.  The area of the rectangle is the length times the height to 13 x 9 which is 117 $m^{2}$