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  • 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 11

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Question 1
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, CA and AB respectively, then
A
$ \displaystyle \frac{1}{{{p}^{2}}}=\frac{1}{{{b}^{2}}}-\frac{1}{{{a}^{2}}}$
B
$ \displaystyle \frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}$
C
$ \displaystyle \frac{1}{{{p}^{2}}}+\frac{1}{{{a}^{2}}}=\frac{1}{{{b}^{2}}}$
D
$ \displaystyle \frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}$
Question 1 Explanation:
geometry-and-mensuration-test-11-qestion-1-pic-1
cat-geometry-and-mensuration-3-png
Question 2
$ \displaystyle \begin{array}{l}If\vartriangle ABC\text{ }is\text{ }similar\text{ }to\vartriangle DEF\text{ }such\text{ }that\text{ }BC=\text{ }3\text{ }cm,\text{ }\\EF=\text{ }4cm\text{ }and\text{ }area\text{ }of\vartriangle ABC=\text{ }54\text{ }c{{m}^{2}},\text{ }\\then\text{ }the\text{ }area\text{ }of\vartriangle DEF\text{ }is:\end{array}$
A
66 cm2
B
78 cm2
C
96 cm2
D
54 cm2
Question 2 Explanation:
In case of similar triangles, the ratio of the areas of the triangles is equal to the square of the sides in proportion.
The ratio of the area of ΔABC  to ΔDEF = 32: 42 =  9:16
The Area of ΔDEF= (16/9)x54 = 96 cm2 Thus, the correct option (c)
Question 3
$ \displaystyle \begin{array}{l}In\,ABC,\angle A=\text{ }{{90}^{o}}and\,AD\bot BC\,where\text{ }D\text{ }lies\text{ }on\text{ }BC.\text{ }\\If\text{ }BC=\text{ }8\text{ }cm,\text{ }AC=\text{ }6cm,\text{ }\\then\,\vartriangle ABC:\,\vartriangle ACD=\text{ }?\end{array}$
A
4: 3
B
25: 16
C
16: 9
D
25: 9
Question 3 Explanation:
geometry-and-mensuration-test-11-qestion31-pic-1
From the figure the ΔABC and ΔACD are similar triangles by AAA similarity.
In case of similar triangles, the ratio of the areas of the triangles is equal to the square of the sides in proportion.
We have ΔABC/ΔACD =82/62= 16/9
Question 4
The areas of two similar triangles ABC and DEF are 20 cm2 and 45 cm2 respectively. If AB= 5cm, then DE is equal to:
A
6.5 cm
B
7.5 cm
C
8.5 cm
D
5.5 cm
Question 4 Explanation:
In case of similar triangles, the ratio of the areas of the triangles is equal to the square of the sides in proportion.
Hence we have AB2 /DE2 = 20/45 = 4/9
AB/DE = 2/3
Now if AB = 5 cm, then DE = 5 x 3/2 = 7.5cm
Question 5
cat-geometry-and-mensuration-5-png-1
A
130o
B
80o
C
100o
D
120o
Question 5 Explanation:
geometry-and-mensuration-test-11-qestion-5-pic-1
We have ∠ABC + ∠BAC + ∠ACB = 1800
=> 5∠ ACB + 3∠ACB + ∠ ACB = 1800
=> 9 ∠ ACB = 1800
=>∠ ACB = 200
So ∠ ABC = 5 ∠ ACB = 5 × 20 = 1000.
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