SOLUTION: find the dimensions of the figure. triangle; area is 12 cm squared, base is x and the height is x+2 cm rectangle; area is 160ft squared, length is x ft.and the width is x-12 ft.

Algebra ->  Triangles -> SOLUTION: find the dimensions of the figure. triangle; area is 12 cm squared, base is x and the height is x+2 cm rectangle; area is 160ft squared, length is x ft.and the width is x-12 ft.      Log On


   

Question 195281: find the dimensions of the figure.
triangle; area is 12 cm squared, base is x and the height is x+2 cm
rectangle; area is 160ft squared, length is x ft.and the width is x-12 ft.
Answer by honey143(2) About Me  (Show Source):
You can put this solution on YOUR website!


1) Area of Triangle = (1/2)base x height


Substituting given:
12cm%5E2=%281%2F2%29%28x%29%28x%2B2%29
Cross multiply/ expand:
12%2A2=x%2A2%2B2x
Combine all terms:
x%5E2%2B2x-24=0
%28x%2B6%29%28x-4%29=0
x=-6, disregard
highlight%28red%28x=4cm%29%29, base
Also, 4%2B2=highlight%28red%286cm%29%29, height

Check,
12cm%5E2=%281%2F2%29%284%29%286%29
12cm%5E2=%281%2F2%2924cm%5E2
12cm%5E2=12cm%5E2


2) Area of Rectangle = Length x Width

Substitue given:
160ft%5E2=%28x%29%28x-12%29
160=x%5E2-12x
x%5E2-12x-160=0
%28x%2B8%29%28x-20%29=0
x=-8, disregard "-"
highlight%28red%28x=20ft%29%29, Length
Also, 20-12=highlight%28red%288ft%29%29, Width

Check,
160ft%5E2=20%2A8
160ft%5E2=160ft%5E2