A long time ago Dulani found an island shaped like a triangle with three straight shores of length 3 km 4 km and 5 km.He said no
body could come within 1km of his shore. What was the area of his exclusion zone?
1 answer:
To find the area of his exclusion zone you would need to understand that a triangle with dimensions of 3, 4, and 5 represent a right triangle.
This means the exclusion zone would be applied to the base and the height of the triangular space.
You would add 2 km to the 3 km, and 2 km to the 4 km to create a new height of 5 km and a new base of 6 km.
Please see the attached picture to understand this.
You will find the area of the total space created by the new triangle and subtract the space represented by the original triangle to find the area of the exclusion zone.
(1/2 x 6 x 5) - (1/2 x 4 x 3)
15 km² -6 km² equals 9 km².
The exclusion space is 9 km².
This means the exclusion zone would be applied to the base and the height of the triangular space.
You would add 2 km to the 3 km, and 2 km to the 4 km to create a new height of 5 km and a new base of 6 km.
Please see the attached picture to understand this.
You will find the area of the total space created by the new triangle and subtract the space represented by the original triangle to find the area of the exclusion zone.
(1/2 x 6 x 5) - (1/2 x 4 x 3)
15 km² -6 km² equals 9 km².
The exclusion space is 9 km².
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The complete question in the attached figure
we know that
angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°
the answer is
x=147°
y=33°
we know that
angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°
the answer is
x=147°
y=33°