[2 Mark Question Answer]

Question 12 Marks

A man goes 15 m due west and then 8 m due north. How far is he from the starting point?

Answer

17 m
$\left[\right.$ Hint. $A C=\sqrt{A B^2+B C^2}$

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Question 22 Marks

A rectangular field is 40 m long and 30 m broad. Find the length of its diagonal.

Answer

50 m

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Question 32 Marks

In a rhombus ABCD , prove that $AC ^2+ BD ^2=4 AB ^2$.

Answer

self

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Question 42 Marks

The diagram shows a nest of 4 squares set one within another. The side of the outer most square is 20 cm. The midpoints of the sides are joined to give a second square and the process repeated to give the third and fourth squares. Find the length of a side of the smallest square.

Answer

$5 \sqrt{2} cm$

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Question 52 Marks

A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Answer

0.8 m

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Question 62 Marks

For going to a city $B$ from city $A$, there is a route via city $C$ such that $A C \perp C B$, $AC =2 x km$ and $CB =2(x+7) km$. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.

Answer

8 km

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Question 72 Marks

In a rhombus $A B C D$, prove that $A C^2+B D^2=4 A B^2$.

Answer

self

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Question 82 Marks

From the given figure, find the area of trapezium ABCD.