Question 266645
Let the height = h.
base = h + 10
area = 28
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The area of a triangle has the formula
{{{A = (1/2)bh}}}
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from the given information, we get
{{{28 = (1/2)*(h)*(h+10)}}}
multiply both sides by 2 to get
{{{56 = h(h+10)}}}
distribute to get
{{{56 = h^2 + 10h}}}
set = 0 to get
{{{0 = h^2 + 10h - 56}}}
factor to get
{{{0 = (h+14)(h-4)}}}
solving we get
h = -14
and
h = 4
we can't use the -14, so our only answer is
h = 4 cm