(a) In the diagram, < PTQ = < PSR = 90°, /PQ/ = 10 cm, /PS/ = 14.4 cm and /TQ/ = 6 cm. Calculate the area of the quadrilateral QRST. (b) Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangleto that of the square.

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(a) In the diagram, < PTQ = < PSR = 90°, /PQ/ = 10 cm, /PS/ = 14.4 cm and ...

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(a)
In the diagram, < PTQ = < PSR = 90°, /PQ/ = 10 cm, /PS/ = 14.4 cm and /TQ/ = 6 cm. Calculate the area of the quadrilateral QRST.
(b) Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangle to that of the square.

Explanation

(a)

(P T)^{2} + (T Q)^{2} = (P Q)^{2}

(P T)^{2} + 6^{2} = 10^{2}

(P T)^{2} = 100 - 36 = 64

∴ P T = 8 c m

∴ \frac{8}{6} = \frac{14.4}{S R}

S R = \frac{6 \times 14.4}{8}

S R = 10.8 c m

Area of the quadrilateral QRST =

\frac{1}{2} (6 + 10.8) \times 6.4

53.76 c m^{2}

(b) Opp sides of a square =

(\frac{(100 - 10) x}{100} = 0.9 x

other two sides of the square =

\frac{(100 + 15) x}{100} = 1.15 x

Area of the square :

x \times x = x^{2}

Area of the rectangle :

0.9 x \times 1.15 x = 1.035 x^{2}

∴ The ratio of the area of the rectangle to the square = 1.035 x^{2} : x^{2}

1.035 : 1

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