SOLUTION: hi I have a question and I am unable to answer it so here goes: Show that the area of this shape can be written as {{{ 5x^2 + 4x- 9 }}} Now the shape is of a letter L an

Algebra ->  Surface-area -> SOLUTION: hi I have a question and I am unable to answer it so here goes: Show that the area of this shape can be written as {{{ 5x^2 + 4x- 9 }}} Now the shape is of a letter L an      Log On


   

Question 773088: hi
I have a question and I am unable to answer it so here goes:
Show that the area of this shape can be written as +5x%5E2+%2B+4x-+9+
Now the shape is of a letter L and all angles are 90 degrees
4 measurements are shown against the 4 x Sides:
LHS +2x%5E2+%2B+3+
Top +2x%5E2+%2B+1+
Bottom +3x+-+5+
RHS Smaller side +x+%2B+2+
Unsure how to work this out as the answer I get is +5x%5E2+-+9+ I don't get the +4x+
I'm I doing something wrong
Thanks
MJ
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This shape is like a rectangle which is missing an upper-right rectangle piece. We can find some projected length distances to find the missing rectangle's width and height.

DRAW the figure so you see what my description is.
Let u=%283x-5%29-%282x%5E2%2B1%29 and let v=%282x%5E2%2B3%29-%28x%2B2%29
The area of the missing rectangular piece is u%2Av.

First find actual u and v in their simplified form; then, find the area of u*v.
u=3x-5-2x%5E2-1=3x-2x%5E2-6
and
v=2x%5E2%2B3-x-2=2x%5E2-x%2B1
highlight%28uv=%28-2x%5E2%2B3x-6%29%282x%5E2-x%2B1%29%29

The L+%2B+uv+=+%282x%5E2%2B3%29%283x-5%29
and just the L by itself would be :
The L=%282x%5E2%2B3%29%283x-5%29-uv
highlight%28L=%282x%5E2%2B3%29%283x-5%29-%28-2x%5E2%2B3x-6%29%282x%5E2-x%2B1%29%29 square units
.
.
That should simplify to highlight%284x%5E4-2x%5E3-3x%5E2-9%29
I just do not get what you report it should be.