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The formula for the area of a trapezium is as follows:
<span>area=<span>12</span>(a+b)h
</span>
Let a be the shorter base. Then a = h + 3.
Let b be the longer base. Then b = h + 7.
Substituting these values for a and b in the general formula gives:
<span>
area = 225 = <span>12</span>(h+3+h+7)h = <span>h^2</span>+5h</span>
So you need to solve the following quadratic:
<span><span>h^2</span>+5h−225=0</span>
Step 1: Use quadratic formula with a=1, b=5, c=-225.
<span>h=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a</span></span></span><span>h=<span><span><span>−<span>(5)</span></span>±<span>√<span><span><span>(5)</span>2</span>−<span><span>4<span>(1)</span></span><span>(<span>−225</span>)</span></span></span></span></span><span>2<span>(1)</span></span></span></span><span>h=<span><span><span>−5</span>±<span>√925</span></span>2</span></span><span><span>h=<span><span><span>−5/</span>2</span>+<span><span><span><span>5/2</span><span>√37</span></span><span> or </span></span>h</span></span></span>=<span><span><span>−5/</span>2</span>+<span><span><span>−5/</span>2</span><span>√37
</span></span></span></span>Answer:<span><span>h=<span><span><span>−5/</span>2</span>+<span><span><span><span>52</span><span>√37</span></span><span> or </span></span>h</span></span></span>=<span><span><span>−5/</span>2</span>+<span><span><span>−5/</span>2</span><span>√<span>37</span></span></span></span></span>
if you isolate y in the top equation to get y=5x+6 then you can substiture y for 5x+6 in the bottom equation because thats what y equals
as of now you have -3x+6(5x+6)=-12 but if you use the distrubite property you would get -3x+30x+36=-12
then if you subtract 36 from both sides you would get -3x+30x=-48 then combine like terms to get 27x=-48 then divide both sides by 27 to get
or x≈1.8