Geometry and Mensuration: Test 25

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Geometry and Mensuration: Test 25

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Question 1

R and S are two points on the sides PT and QT respectively of ΔPQR such that RS= 18 cm, TS= 5 cm and ÐRST= 90^o. If tan ÐPQR= 3.6, then PT: TR =

A	QT: 2 TS
B	2 TS: QT
C	2 QT: TS
D	TS: 2 QT

Question 1 Explanation:

$ \displaystyle \begin{array}{l}\angle \,RST={{90}^{o}}\\RS=18\,cm\\TS=5\,cm\\\therefore \,\,\tan \,T=\frac{RS}{TS}=\frac{18}{5}=3.6\\\tan \,\angle PQR=3.6\\\therefore \angle T=\angle Q\\\therefore PT=PQ\\\angle T+\angle R={{90}^{o}}\\\Rightarrow 2\,\angle T+2\,\angle R={{180}^{o}}\\\angle T+\angle P+\angle Q={{180}^{o}}\\\Rightarrow \,2T+\angle P={{180}^{o}}\\\therefore \,\,\angle P=2\,\angle R\\\therefore \,\frac{PT}{TQ}=\frac{2TR}{TS}\end{array}$

Question 2

BL and CM are medians of ΔABC right-angled at A and BC= 5cm. If BL = 8cm, then the length of CM is

A	√61/2cm
B	√48/2cm
C	10√2cm
D	4 cm

Question 2 Explanation:

Question 3

ABCD is a rectangle where the ratio of the lengths of AB and BC is 3: 2. If P is the mid-point of AB, then the value of sin ∠CPB is

A	3/5
B	2/5
C	3/4
D	4/5

Question 3 Explanation:

Question 4

PQRS is a square, T is the mid-point of PQ and M is the mid-point of QR. PM and ST are joined and they meet at L. Then which of the following is correct?

A	TP: TL= 1: 2
B	PM = TS
C	∠PMS = ∠PMQ
D	∠PTS = ∠QPM

Question 4 Explanation:

$ \displaystyle \begin{array}{l}If\,\,\,PQ=2x,\,\,then\,\,QM=x\\\therefore \,\,PM=\sqrt{4{{x}^{2}}+{{x}^{2}}}=\sqrt{5}x\\Similarly,\\TS=\sqrt{4{{x}^{2}}+{{x}^{2}}}=\sqrt{5}x\end{array}$
Hence PM=TS

Question 5

If the sums of the interior angles of a regular polygon be 1080^o, the number of sides of the polygon is