Answer:
Hi,
Step-by-step explanation:
Let say a the base of the triangle A and b the base of the triangle B.
[tex]a)\\\left\{\begin{array}{ccc}\dfrac{a*x}{2}&=&30\\\dfrac{b*(x+3)}{2}&=&32\\b=a-4\\\end{arraqy}\right.\\\\(i): a=\dfrac{60}{x}\\\\(ii): b=\dfrac{64}{x+3}\\\\b)\\\dfrac{64}{x+3}=\dfrac{60}{x}-4\\\\64x=(60-4x)*(x+3)\\\\4x^2+16x-180=0\\\\x^2+4x-45=0\\\\\Delta=16+4*45=196=14^2\\x=\dfrac{-4+14}{2}=5\ or\ x=\dfrac{-4-14}{2}=-9\ (impossible)\\So\ x=5,\ a=\dfrac{60}{5}=12, b=\dfrac{64}{5+3}=8\\\\Area\ of\ A=12*5/2=30\\Area\ of\ B=8*8/2=32\\\\Height\ of\ triangle\ B=x+3=5+3=8.\\[/tex]
