Geometry and Mensuration: Test 11

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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

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