Question 1185595
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Parallelogram with area 88 and one side (AB) 8, so altitude (DE) is 88/8=11; one diagonal (the short one, BD) is 12.<br>
{{{drawing(400,400,-1,13,-1,13
,line(0,0,8,0),line(8,0,11,11),line(11,11,3,11),line(3,11,0,0)
,line(3,0,3,11),line(8,0,3,11),line(0,0,11,11)
,line(8,0,11,0),line(11,0,11,11)
,locate(-.5,-.25,"A(0,0)"),locate(8,-.25,"B(8,0)"),locate(10,12,"C(16-x,11)"),locate(2,12,"D(8-x,11)"),locate(2,-.25,"E(8-x,0)"),locate(10,-.25,"F(16-x,0)")
,locate(1,6,y),locate(8,9,z),locate(3,6,11),locate(7,3,12)
,locate(1.5,.75,"8-x"),locate(5,.75,x)
)}}}<br>
a) Find the length of the other side (y).<br>
(1) Use the Pythagorean Theorem in triangle BED to find x ;
(2) calculate 8-x (AE);
(3) Use the Pythagorean Theorem in triangle AED to find y.<br>
b) Find the length of the other diagonal (AC).<br>
Use the Pythagorean Theorem in triangle AFC to find z.<br>
c) Find the altitude to the longer side of the parallelogram.<br>
It's the area 88, divided by the length of the other side, y.<br>