SOLUTION: A right-angled triangle has an area of 30cm^2. The width of the triangle is n+3cm. The height is 4cm less than the width. Find the value of n.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A right-angled triangle has an area of 30cm^2. The width of the triangle is n+3cm. The height is 4cm less than the width. Find the value of n.      Log On


   

Question 923837: A right-angled triangle has an area of 30cm^2. The width of the triangle is n+3cm. The height is 4cm less than the width. Find the value of n.
Answer by MathLover1(20850) About Me  (Show Source):
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A right-angled triangle has an area of 30cm%5E2:
A=%28width%2Aheight%29%2F2 => %28width%2Aheight%29%2F2=30cm%5E2
if the width of the triangle is W=n%2B3cm, and the height h is 4cm less than the width, then we have
W=n%2B3cm
h=n%2B3cm-4cm=>h=n-1cm
go to %28width%2Aheight%29%2F2=30, plug in W=n%2B3cm and h=n-1cm
%28%28n%2B3%29%2A%28n-1%29%29%2F2=30cm%5E2
%28n%2B3cm%29%2A%28n-1cm%29=60cm%5E2
n%5E2-n%2Acm%2B3n%2Acm-3cm%5E2=60
n%5E2%2B2n%2Acm-3cm%5E2-60cm%5E2=0
n%5E2%2B2n%2Acm-63cm%5E2=0.........write 2n%2Acm as 9n%2Acm-7n%2Acm
n%5E2%2B9n%2Acm-7n%2Acm-63cm%5E2+=+0...group
%28n%5E2%2B9n%2Acm%29-%287n%2Acm%2B63cm%5E2%29+=+0..factor
n%28n%2B9cm%29-7cm%28n%2B9cm%29+=+0
%28n-7cm%29%28n%2B9cm%29+=+0
we need only positive solution and it is n-7cm+=+0=>highlight%28n=7cm%29
now find
width=n%2B3cm=>width=7cm%2B3cm=>width=10cm
height=n-1cm=>h=7cm-1cm=>h=6cm