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• This is an assessment test.
• These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
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## Geometry and Mensuration: Test 23

Congratulations - you have completed Geometry and Mensuration: Test 23.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
 Question 1
If the medians of two equilateral triangles are in the ratio 1:2 then what is the ratio of their sides?
 A 1: 2 B 2: 3 C 3: 2 D âˆš3: âˆš2
Question 1 Explanation:
$\displaystyle \begin{array}{l}Median\text{ }of\text{ }an\text{ }equilateral\text{ }triangle=\frac{\sqrt{3}}{2}a\\By\text{ }given\text{ }condition\\\frac{\frac{\sqrt{3}}{2}{{a}_{1}}}{\frac{\sqrt{3}}{2}{{a}_{2}}}=\frac{1}{2}\\\therefore \,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{2}\end{array}$
 Question 2
The hypotenuse of a right triangle is 3âˆš10 unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9âˆš5 unit. What are the lengths of the smaller and longer sides of the right triangle respectively?
 A 5 unit and 9 units B 5 units and 6 units C 3 units and 9 units D 3 units and 6 units
Question 2 Explanation:
Let the sides be x , y where x<y
x2 + y2 =(3âˆš10)2 = 90
9x2 + 4y2 =(9âˆš5)2 = 405
Solving the two equations
x = 3 and y=9
 Question 3
In the figure given above, PQ = QS and QR = RS. If âˆ SRQ = 100Â°, how many degrees is âˆ QPS?
 A 40Â° B 30Â° C 20Â° D 15Â°
Question 3 Explanation:
 Question 4
ABC is a right angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b and c are the lengths of the sides BC, AC and AB respectively, then which one of the following is correct?
 A (a2 + b2)p2 = a2b2 B a2 + b2 = a2b2p2 C p2= a2 + b2 D p2= a2 â€“b2
Question 4 Explanation:

$\begin{array}{l}\frac{1}{2}pc=\frac{1}{2}ab\,\,\left( Since\text{ }area\text{ }of\text{ }same\text{ }triangles \right)\\{{p}^{2}}{{c}^{2}}={{a}^{2}}{{b}^{2}}\\=>{{p}^{2}}({{a}^{2}}+{{b}^{2}})={{a}^{2}}{{b}^{2}}\end{array}$
 Question 5
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?
 A 20 cm B 24 cm C 25 cm D 28 cm
Question 5 Explanation:

$\begin{array}{l}\because AB||EF||CD\\\frac{EF}{CD}=\frac{EG}{GC}\\=>\frac{EF}{18}=\frac{5}{10}\\=>EF=9\\In\vartriangle ABC\text{ }and\vartriangle EFC\text{ }\left( similar\text{ }triangles \right),\\\frac{EF}{AB}=\frac{EC}{AC}\\=>9/15=15/AC\\AC=(15\times 15)/9=25cm\end{array}$
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