Processing math: 100%

WAEC Mathematics Past Questions & Answers - Page 142

706.

If the perimeter of $\bigtriangleup$ PQR in thr diagram is 24cm, what is the area of $\bigtriangleup$ PRS?

19.5cm²

15.0cm²

13.0cm²

9.3cm²

View answer & explanation

Correct answer is B

Perimeter of $\bigtriangleup$ PQR = PQ + QR + PR

24cm = 6cm + 8cm = PR

24 = 14 + PR

PR = 24 - 14 = 10cm

Area of $\bigtriangleup$ PRS = $\frac{1}{2} \times 10 \times 3cm^3$

= 15cm³

707.

In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.

25^o

65^o

115^o

130^o

View answer & explanation

Correct answer is B

x = 65^o (An interior angle of a cyclic quadrilateral = opposite exterior angle).

708.

In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of $\bigtriangleup$ YZR?

1:2

2:1

1:2

3:1

View answer & explanation

Correct answer is B

From the diagram, XYZQ is a parallelogram. Thus, |YZ| = |XQ| = |PX|; $\bigtriangleup$ PXY, Let the area of XYZQ = A₁, the area of $\bigtriangleup$ PXY

= Area of $\bigtriangleup$ YZR = A₂

Area of $\bigtriangleup$ PQR = A = A₁ + 2A₂

But from similarity of triangles

$\frac{\text{Area of PQR}}{\text{Area of PXY}} = (\frac{PQ}{PX})^2 = (\frac{QR}{XY})^2$

$\frac{A}{A_2} = (\frac{2}{1})^2 = \frac{2}{1}$

A = 4A₂ But, A = A₁ + 2A

A₁ = 4A₂ - 2A₂

A₁ = 2A₂

$\frac{A_1}{A_2}$ = 2

A₁:A₂ = 2:1

Area of XYZQ:Area of $\bigtriangleup$ YZR = 2:1