Question 859080


{{{A = L*W}}}
Now plug in {{{2W+3}}} instead of L
{{{A = (2W+3)*W}}}
{{{65 = 2W^2 + 3W}}}


Now put the equation in standard form.
{{{2W^2 + 3W - 65 = 0}}}


You want to factor. Separate the middle term into two parts:
{{{2W^2 - 10W + 13W - 65 = 0}}}
Factor the sides:
{{{2W(W - 5) + 13(W - 5) = 0}}}
Factor the bracket and what's not in it:
{{{(2W + 13)(W-5) = 0}}}


Now what we have is two options:
{{{2W + 13 = 0}}}, which gives that W equals -6.5, which is clearly not right.
{{{W - 5 = 0}}}, which gives that W equals 5.


Now, from {{{65 = L*W}}}, compute for L.
{{{L = 65/W = 65/5 = 13}}}


Width of the triangle is 5 m and its length is 13 m. Also check.