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Geometry and Mensuration: Test 24

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Question 1
AB, EF and CD are parallel lines. Given that, EF= 5 cm GC = 10 cm, AB = 15 cm and DC = 18 cm. What is the value of AC?
46
A
20 cm
B
24 cm
C
25 cm
D
28 cm
Question 1 Explanation:
47
$ \begin{array}{l}\because AB||EF||CD\\\frac{EF}{CD}=\frac{EG}{GC}\\=>\frac{EF}{18}=\frac{5}{10}\\=>EF=9\\In\vartriangle ABC\text{ }and\vartriangle EFC\text{ }\left( similar\text{ }triangles \right),\\\frac{EF}{AB}=\frac{EC}{AC}\\=>9/15=15/AC\\AC=(15\times 15)/9=25cm\end{array}$
Question 2
In the given triangle, AB is parallel to PQ. AP = c, PC = b, PQ = a, AB = x. What is the value of x?
48
A
$ \displaystyle a+\frac{ab}{c}$
B
$ \displaystyle a+\frac{bc}{a}$
C
$ \displaystyle b+\frac{ca}{b}$
D
$ \displaystyle a+\frac{ac}{b}$
Question 2 Explanation:
$ \begin{array}{l}~ABC\text{ }is\text{ }congruent\text{ }to~PQC,\\\frac{AC}{PC}=\frac{BC}{QC}=\frac{AB}{PQ}\\=>x=\frac{AC\times PQ}{PC}=\frac{(b+c)a}{b}=a+\frac{ac}{b}\end{array}$
Question 3
In the given figure, QR is parallel to AB, DR is parallel to QB. What is the number of distinct pairs of similar triangles?
cat-geometry-and-mensuration-11png-1
A
1
B
2
C
3
D
4
Question 3 Explanation:
49
$ \displaystyle \begin{array}{l}The\text{ }triangles\vartriangle PDR\text{ }and\vartriangle PQB,\vartriangle PQR\text{ }and\vartriangle PAB,\vartriangle DRQ\text{ }and\vartriangle QBA\text{ }are\text{ }similar.\\Thus\text{ }there\text{ }are\text{ }three\text{ }possible\text{ }pairs\text{ }of\text{ }triangles.\\Correct\text{ }option\text{ }is\text{ }\left( c \right).\end{array}$
Question 4
If the angels of a triangle are 30°, 60° and 90°, then what is the ratio of the corresponding sides?
A
1: 2: 3
B
1: 1: √2
C
1: √3: 2
D
1: √2: 2
Question 4 Explanation:
$\begin{array}{l}\tan \,60=\sqrt{3}\\Thus\text{ }the\text{ }ratio\text{ }of\text{ }corresponding\text{ }sides\text{ }=1:\text{ }\surd 3:\text{ }2\\\end{array}$
Question 5
I is the incentre of ∆ABC, ABC= 60o and ACB= 50o. The BIC is:
A
55o
B
125o
C
70o
D
65o
Question 5 Explanation:
50
$ \displaystyle \begin{array}{l}\angle BIC\text{ }=~=\text{ }180\text{ }\frac{1}{2}\left( ABC+ACB \right)\\\text{=180 - }30-25\text{ }=\text{ }125.\\Correct\text{ }option\text{ }is\text{ }\left( b \right)\end{array}$
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