Question

11(a) If (3p+4q)/(3p-4q)=2, find p:q
(b) The diagram shows the cross section of a bridge with a semi circular hollow in the middle. If the perimeter of the cross section is 34cm, calculate the: (i) length PQ (ii) area of the cross section [Take π=22/7]

Accepted Answer

(a) (3p+4q)/(3p-4q)=2
3p+4q = 2(3p-4q)
3p+4q = 6p-8q
4q+8q = 6p-3p
12q = 3p
p:q = 12:3 = 4:1

(b) Let x = radius of the semicircle. Length PQ = 2+x+x+2 = 4+2x
Circumference of semicircle = πr = πx = (22/7)x
Perimeter of cross-section = 4+4+4+2x+(22/7)x = 34
16x+22x = (34-16)×7  [multiplying through by 7]
Actually: 16+2x+(22/7)x=34 → 2x+(22/7)x=18 → (14x+22x)/7=18 → 36x=126 → x=3.5cm
(i) Length PQ = 4+2(3.5) = 4+7 = 11cm

(ii) Area of cross-section = Area of rectangle PQRU - Area of semicircle
= 11×4 - (22/7)×(3.5)²×½
= 44 - 19.25
= 24.70cm²

WAEC Mathematics 2016 Theory — Question 11

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