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On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1

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by BTGModeratorVI » Thu Dec 03, 2020 2:50 pm

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On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

Answer: D
Source: official guide
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Re: On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters.

by Scott@TargetTestPrep » Sun Dec 06, 2020 8:55 am
BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:50 pm
 On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

Answer: D
Source: official guide
Solution:

Since 1 cm represents 3 meters, the sides, in meters, of the triangular piece of land are 5 x 3 = 15, 12 x 3 = 36 and 13 x 3 = 39. Furthermore, since 5-12-13 is a right triangle, 15-36-39 is also a right triangle. Therefore, the area of the triangular piece of land is half of the product of its legs (the two shorter sides), that is,

Area = ½ bh = ½ x 36 x 15 = 18 x 15 = 270 m^2

Answer: D

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