How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #5 #, and #5 #?

Answer 1

#A=2sqrt21approx9.1652#

Heron's formula states that for a triangle with sides #a,b,c# and a semiperimeter #s=(a+b+c)/2#, the area of the triangle is
#A=sqrt(s(s-a)(s-b)(s-c))#

Here, we know that

#s=(4+5+5)/2=7#

which gives an area of

#A=sqrt(7(7-4)(7-5)(7-5))#
#A=sqrt(7xx3xx2xx2)#
#A=2sqrt21approx9.1652#
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Answer 2

To use Heron's formula to find the area of a triangle with sides of lengths ( a = 4 ), ( b = 5 ), and ( c = 5 ), follow these steps:

  1. Calculate the semi-perimeter of the triangle, denoted by ( s ), using the formula: [ s = \frac{a + b + c}{2} ]

  2. Compute the expression under the square root in Heron's formula, denoted by ( \Delta ), using the semi-perimeter calculated in step 1: [ \Delta = s(s - a)(s - b)(s - c) ]

  3. Take the square root of ( \Delta ) to find the area of the triangle: [ \text{Area} = \sqrt{\Delta} ]

Let's compute it:

Step 1: [ s = \frac{4 + 5 + 5}{2} = \frac{14}{2} = 7 ]

Step 2: [ \Delta = 7(7 - 4)(7 - 5)(7 - 5) ] [ = 7(3)(2)(2) = 84 ]

Step 3: [ \text{Area} = \sqrt{84} ]

Now, you can simplify ( \sqrt{84} ) to find the exact area of the triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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