SOLUTION: We have a rectangle and a right-angled triangle. All measurements are in centimeters. The area of the rectangle is greater than the area of the triangle. Find the set of possibl

Algebra ->  Inequalities -> SOLUTION: We have a rectangle and a right-angled triangle. All measurements are in centimeters. The area of the rectangle is greater than the area of the triangle. Find the set of possibl      Log On


   

Question 1150491: We have a rectangle and a right-angled triangle.
All measurements are in centimeters.
The area of the rectangle is greater than the area of the triangle.
Find the set of possible values for x when:
rectangle length: 5x-6
rectangle width: x-1
triangle height: 2x
triangle base: x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
rectangle length: 5x-6
rectangle width: x-1
so, the area of the rectangle is:%285x-6%29%28x-1%29

triangle height: 2x
triangle base: x
so, the area of the triangle is: %28x%2A2x%29%2F2->x%5E2

if the area of the rectangle is greater than the area of the triangle, we have:
%285x-6%29%28x-1%29%3Ex%5E2.........solve for x

5x%5E2-6x-5x%2B6%3Ex%5E2
5x%5E2-x%5E2-11x%2B6%3E0
4x%5E2-11x%2B6%3E0.....factor completely
4x%5E2-8x-3x%2B6%3E0
%284x%5E2-8x%29-%283x-6%29%3E0
4x%28x-2%29-3%28x-2%29%3E0
%28x+-+2%29+%284+x+-+3%29%3E0
solutions
if %28x+-+2%29%3E0=>x%3E2
if +%284+x+-+3%29%3E0=>4x%3E3=>x%3E3%2F4

the set of possible values for x:
all x%3E2
all x%3E3%2F4-> using first greater number (x=1) will not make a statement %285x-6%29%28x-1%29%3Ex%5E2 true; exclude x=1