What length of fence is needed to surround the garden in the following geometry question?A garden is in the shape of a right triangle. The base of the triangle is 12m and the garden covers an area...

What length of fence is needed to surround the garden in the following geometry question?

A garden is in the shape of a right triangle. The base of the triangle is 12m and the garden covers an area of 30m2.

Asked on by tealseal

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We know that theb area of the right angle triangle is:

A = (1/2) * base * height

==> A = (1/2) * b * h

Given:

 the base (b) = 12 m

the area (A)= 30 m

Then we can calculate the height:

30 = (1/2) * 12 * h

30 = 6 h

==> h = 30/6 = 5 m

Then the height of the triangle is:

h = 5 m

Now we have the measures of both sides of the triangle, then we can obtain the third side (s) using the foluma:

Hypetenuse^2 = base^2 + height^2

==> s^2 = 12^2 + 5^2

==> s = sqrt(144+ 25) = sqrt(169) = 13 m

==> S = 13m

Now we have all 3 sides .

The fence needed should equal the perimeter of the triangle:

P = 12+ 13 + 5= 30 m

Then length of the fence needed is 30 m

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

The correct answer is that you will need 30 meters of fencing to enclose the entire garden.  Here is how to get this answer:

First, we know that the area of a triangle is found by the equation

Area = .5 (base*height)

We have the area and the base so we can find the height.

30 = .5 (12*h) if h is the height.

30 = 6h

h = 5

This means that the height of the triangle is 5 meters.

So now we have a right triangle with legs of 12 and 5 meters.  We now use the Pythagorean Theorem

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

c = 13

So now we know that the hypotenuse is 13 meters while the legs are 5 and 12 meters.

Added together, that gives us a total perimeter of 30 meters.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The information given is that the garden has the shape of a right angle. 

The base of the grden has 12meter. The area of the garden is 30 m^2.

Therefore if one side of the right angle is 12, then using (1/2) base *height = area of the triangle, we get (1/2)(12)*h = 30. So h = 60/12 =5 meter.

Therefore by using Pythagoras theorem, the hypotenuse side of the garden should measure = sqrt{base^2+h^2} = sqrt(12^2+5^2} = sqrt(144+25) = 13 meter.

Therefore the sides of the garden being 5 meter, 12meter and 13 meter, its perimeter  = (5+12+13) meter=30 meter. So the garden requires a fencing of 30 meter.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The information given is that the garden has the shape of a right angle. 

The base of the grden has 12meter. The area of the garden is 30 m^2.

Therefore if one side of the right angle is 12, then using (1/2) base *height = area of the triangle, we get (1/2)(12)*h = 30. So h = 60/12 =5 meter.

Therefore by using Pythagoras theorem, the hypotenuse side of the garden should measure = sqrt{base^2+h^2} = sqrt(12^2+5^2} = sqrt(144+25) = 13 meter.

Therefore the sides of the garden being 5 meter, 12meter and 13 meter, its perimeter  = (5+12+13) meter=30 meter. So the garden requires a fencing of 30 meter.

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