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 cm, BC=4 cm, and angle ABC= $90^{\circ} .$
The area of the plot in sq. km is 37.5 sq. km.

True

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False

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Solution

The correct option is A True
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

Area of plot = $\frac{1}{2} \times L e n g t h_{A B} \times L e n g t h_{B C}$ (Area of triangle = $\frac{1}{2} b a s e \times h e i g h t$ )
Area of plot = $\frac{1}{2} \times (0.75) \times 1$
Area of plot = $0.375$ $k m^{2}$

Suggest Corrections

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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=3 cm, BC=4 cm, and angle ABC=90∘.The area of the plot in sq. km is 37.5 sq. km.

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 cm, BC=4 cm, and angle ABC= $90^{\circ} .$
The area of the plot in sq. km is 37.5 sq. km.