[1 Mark Question Answer]

Question 11 Mark

On a map drawn to a scale of $1 : 2,50,000;$ a triangular plot of land has the following measurements $: AB = 3\ cm, BC = 4\ cm$ and angle $ABC = 90^\circ.$
Calculate : the area of the plot in sq. km.

Answer

The area of the plot in sq. km
$=\frac{1}{2} \times A B \times B C$
$=\frac{1}{2} \times 7.5 \times 10$
$= 37.5$ sq. km

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Question 21 Mark

A model of an aeroplane is made to a scale of 1 : 400. Calculate :

the length, in m, of the aeroplane, if length of its model is 16 cm.

Answer

The ratio of the length of two corresponding sides of two similar traingles.
A model of an aeroplane is made to a scale of 1 : 400
So, the length of the aeroplane = $400 \times \frac{16}{100}=64 m$

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Question 31 Mark

A model of an aeroplane is made to a scale of 1 : 400. Calculate :
the length, in cm, of the model; if the length of the aeroplane is 40 m

Answer

The ratio of the length of two corresponding sides of two similar triangles.
A model of an aeroplane is made to a scale of 1 : 400.
So, the length of the model = $\frac{1}{400} \times 4000=10 cm$

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Question 41 Mark

A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C' Calculate : the length of AB, if A' B' = 6 cm.

Answer

Given that ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C'
A' B' = 6cm
So, AB (2.5) = A'B'
$\Rightarrow$ AB (2.5) = 6
$\Rightarrow$ AB = 2.4 cm

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Question 51 Mark

Area of two similar triangles are 98 sq.cm and 128 sq.cm. Find the ratio between the lengths
of their corresponding sides.

Answer

Required ratio $=\sqrt{\frac{98}{128}}=\frac{\sqrt{49}}{64}=\frac{7}{8}$

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Question 61 Mark

The ratio between the corresponding sides of two similar triangles is 2 is to 5. Find the ratio
between the areas of these triangles.

Answer

We know that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
Required ratio = $\frac{2^2}{5^2}=\frac{4}{25}$

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Question 71 Mark

In the following figure, point D divides AB in the ratio 3 : 5. Find : $\frac{A D}{A B}$

Answer

Given that $\frac{A D}{D B}=\frac{3}{5}$
So, $\frac{A D}{A B}=\frac{3}{8}$

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Mathematics [1 Mark Question Answer]

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