Question 1150827
the diagonal of a rectangle is 15cm, and the perimeter is 38cm. what is the area?
<pre>I agree with @IKLEYN. Why spend a "day" solving a problem when it can take just 2 minutes?  And, almost no-one who 
I've ever dealt with, wants to use the quadratic equation or "Completing the Square" to solve a quadratic equation.

Let length and width be L and W, respectively
With perimeter being 38 cm, we get: 2(L + W) = 2(19)____L + W = 19 ---- eq (i)
With diagonal being 15 cm, we also get: {{{matrix(1,3, L^2 + W^2, "=", 15^2)}}} ----- eq (ii)
{{{matrix(1,7, L^2 + 2LW + W^2, "=", 19^2,"______", L^2 + W^2, "=", 19^2  -  2LW)}}} ------ Squaring eq (i) ------ eq (iii)
{{{matrix(1,3, 15^2, "=", 19^2 - 2LW)}}} ------- Substituting {{{matrix(1,3, 15^2, for, L^2 + W^2)}}}
{{{matrix(1,3, 15^2 - 19^2, "=", - 2LW)}}}
We then get: {{{highlight_green(matrix(1,8, AREA, "or", LW, "=", (15^2 - 19^2)/(- 2), "=", 68, cm^2))}}}