State true or false:
On a map drawn to a scale of $1 : 25, 0000$ ; a triangular plot of land has the following measurements AB= $3 c m$ , $B C = 4$ cm, and angle ABC= $90^{\circ} .$
The actual lengths of AB and BC in km are $7.5$ km and $10$ km.

True

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False

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Solution

The correct option is B False
Scaling factor = $\frac{L e n g t h o f m o d e l}{L e n g t h o f b u i l d i n g}$

$\frac{1}{250000} = \frac{A B}{L e n g t h_{A B}}$

$L e n g t h_{A B} = 250000 \times 3$

$L e n g t h_{A B} = 750000$

$L e n g t h_{A B} = 0.75$ km

$\frac{1}{250000} = \frac{B C}{L e n g t h_{B C}}$

$L e n g t h_{B C} = 250000 \times 4$

$L e n g t h_{B C} = 1000000$

$L e n g t h_{B C} = 1$ km

Given statement is false.

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State true or false:On a map drawn to a scale of 1:25,0000; a triangular plot of land has the following measurements AB=3cm, BC=4 cm, and angle ABC=90∘.The actual lengths of AB and BC in km are 7.5 km and 10 km.

The correct option is B FalseScaling factor = LengthofmodelLengthofbuilding1250000=ABLengthABLengthAB=250000×3LengthAB=750000LengthAB=0.75 km1250000=BCLengthBCLengthBC=250000×4LengthBC=1000000LengthBC=1 kmGiven statement is false.

State true or false:
On a map drawn to a scale of $1 : 25, 0000$ ; a triangular plot of land has the following measurements AB= $3 c m$ , $B C = 4$ cm, and angle ABC= $90^{\circ} .$
The actual lengths of AB and BC in km are $7.5$ km and $10$ km.