A triangular traffic island has a base half as long as its height. The island has an area of 169 square meters. How do you find the base and the height?

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Answer 1 · 2017-05-05T03:39:32

#Base = 13#
#Height = 26#

My method was to just estimate:

#15 * 30 =# N/a
#14 * 28 =# N/a
#13 * 26 = 388# #(169 * 2)#

Answer 2 · 2017-05-05T03:48:57

The base is #13m# and the height is #26m#.

The formula for area of a triangle is:

#A=(hxxb)/2#, where #A=#Area, #h=#height, and #b=#base.

Since we know that the base is half as long as the height, we can represent the height as #2b#.

Hence, in the formula we could write:

#A=(2bxxb)/2#

We know that the area is #169m^2#. Hence:

#169=(2bxxb)/2#

#169=(2b^2)/2#

#169=(1cancel2b^2)/(1cancel2)#

#169=b^2#

Determine the square root of both sides.

#sqrt169=b#

#sqrt(13*13)=b#

#13=b# (taken to be positive since it is a measurement of a physical entity)

Since the base is #13#, the height is:

#h=2b#

#h=2xx13#

#h=26#