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## Geometry and Mensuration: Level 1 Test 4

Congratulations - you have completed Geometry and Mensuration: Level 1 Test 4. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
In a triangle ΔABC, the side BC is extended up to D. Such that CD= AC, if ∠BAD= 109o and ACB= 72o then the value of ∠ABC is
 A 35o B 60o C 40o D 45o
Question 1 Explanation: $\displaystyle \begin{array}{l}Since,\text{ }AC=CD~\\\angle CAD\text{ }=\angle ADC~=\frac{72}{2}=36\\BAC\text{ }=\text{ }109-36\text{ }=\text{ }73.\\ABC\text{ }=\text{ }180-BAC-ACB\text{ }=\text{ }35.\\Correct\text{ }option\text{ }is\text{ }\left( a \right)\end{array}$
 Question 2
The area of a square is 2.25 cm2. What is its perimeter?
 A 9.0 cms B 6.0 cms C 1.5 cms D 4.5 cms.
Question 2 Explanation: $\displaystyle \begin{array}{l}Perimeter~=\text{ }4~=\sqrt{area}\\\text{=}\,4\times 2.25~=\text{ }4\times 1.5\text{ }=\text{ }6\text{ }cm\\Correct\text{ }option\text{ }is\text{ }\left( b \right)\end{array}$
 Question 3
The length of a rectangle is 20% more than its breadth. What will be the ratio of the area of this rectangle to the area of a square whose side is equal to the breadth of the rectangle?
 A 5: 6 B 6: 5 C 2: 1 D Data inadequate
Question 3 Explanation:
$\begin{array}{l}The\,\,required\,\,ratio\,\,will\,\,be\,\,1.2\times breadt{{h}^{2}}:breadt{{h}^{2}}=6:5\\Correct\,\,option\,\,is\,\,(b)\end{array}$
 Question 4
The sum of three altitudes of a triangle is
 A equal to the sum of three sides B less than the sum of sides C greater than the sum of sides D twice the sum at sides
Question 4 Explanation:
Since the question is based on a geometrical identity it must be valid for all triangles.
Thus we can assume an equilateral triangle of side a cm.
Altitude = √3a/2.
Sum of all altitudes = √3a/2 cm
1.5 X 1.73 a= 2.595a cm
Sum of the three sides = 3a cm.
 Question 5
A rectangular carpet has an area of 120sq. metres and a perimeter of 46 metres. The length of its diagonal (in metres) is:
 A 11 B 13 C 15 D 17
Question 5 Explanation:
$\begin{array}{l}Diagonal=\sqrt{lengt{{h}^{2}}+breadt{{h}^{2}}}\\=\sqrt{{{\left( length+breadth \right)}^{2}}-2\,length\times breadth}\\=\sqrt{{{\left( \frac{46}{2} \right)}^{2}}-2\times 120}=17m\end{array}$
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