Question

高中数学 求用英文解答第二题 谢谢

Answer 1

（1）∵AB is parallel to CD ∴ ∠BAD + ∠ADC =180°
∴ ∠BAP + ∠PAD + ∠ADP + ∠PDC =180°
∵∠APD=90° ∴∠PAD + ∠ADP = 90° ∴ ∠BAP + ∠PDC =90°
∵∠CPD + ∠PDC =90° ∴∠BAP = ∠CPD
∵∠ABP = ∠PCD =90° ∴△ABP∽△PCD
（2）∵BP=x cm, AC=11cm ∴PC=(11-x) cm
∵△ABP∽△PCD ∴AB/PC=BP/CD
∴ 3/(11-x)=x/k ∴x^2-11x+3k=0
(3) Since there exists a real number x satisfying the equation above,
the discriminant must be nonnegative. That is to say, Δ=121-12k≥0.
As a result, k ≤121/12. Considering that k is an integer, we have k ≤ 10.
Namely, the greatest value of k is 10.
(When k = 10, x=5 or x=6. )