如图 等腰直角三角形ABC的腰长AB=BC=8CM 点P在AB上从点A向点B方向移动,过点P作PD平行AC,叫BC于点D,做PE平行BC,交AC于点E当PA为多长时,平行四边形PECD的面积是15平方厘米.
设PA为X cm ,则 PB=（8-X）cm.
∵ △ABC为等腰直角三角形,且PE∥BC,PD∥AB;
∴ ∠BAC=∠PAE=∠BPD=45°∠ABC=∠PBD=∠APE=90°
∴ PA=PE=Xcm BP=BD=(8-X)cm
由图可知S□PECD =S△ABC — S△PBD — S△APE
15 =1/2 ×AB×BC —1/2×BP×BD—1/2×PA×PE
15 =1/2×8×8—1/2×（8-X）×（8-X）—1/2×X×X
15 = 32 —1/2× (8-X)^2 —1/2 × X^2
15 = 32 —1/2×（64-16X-X^2）—1/2× X^2
15 = 32 —32 + 8X —1/2× X^2—1/2× X^2
15 = 8X — X^2
X^2 -8X+15 = 0
(X-3) ×(X-5)= 0
由此可得X=3或者X=5；
所以当X=3或者X=5时,平行四边形PECD的面积是15平方厘米.