BTGModeratorVI wrote: ↑

Tue Mar 03, 2020 6:34 am

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

The key here is to recognize that 5, 12 and 13 represent a Pythagorean triplet, which means the triangle in question is a RIGHT TRIANGLE

So, the drawing has sides 5 cm, 12 cm, and 13 cm . . .

. . . which means the piece of land has sides 15 m, 36 m and 39 m

Area of triangle = (base)(height)/2
Area of land = (36)(15)/2 = 270

Answer: D

ASIDE: Other Pythagorean triplets you should know:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue Mar 03, 2020 6:34 am

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

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