We appreciate your visit to What is the area of a triangle with tex a 25 tex tex b 13 tex and tex c 17 tex A 99 1 units. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the area of a triangle with sides [tex]\( a = 25 \)[/tex], [tex]\( b = 13 \)[/tex], and [tex]\( c = 17 \)[/tex], we can use Heron's formula. Here's a step-by-step approach:
1. Calculate the Semi-perimeter (s):
The semi-perimeter [tex]\( s \)[/tex] is half of the sum of the sides of the triangle.
[tex]\[
s = \frac{a + b + c}{2} = \frac{25 + 13 + 17}{2} = \frac{55}{2} = 27.5
\][/tex]
2. Apply Heron's Formula:
Heron's formula states that the area [tex]\( A \)[/tex] of a triangle with semi-perimeter [tex]\( s \)[/tex] and sides [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] is:
[tex]\[
A = \sqrt{s(s - a)(s - b)(s - c)}
\][/tex]
Substituting the values into the formula:
[tex]\[
A = \sqrt{27.5 \times (27.5 - 25) \times (27.5 - 13) \times (27.5 - 17)}
\][/tex]
[tex]\[
A = \sqrt{27.5 \times 2.5 \times 14.5 \times 10.5}
\][/tex]
Calculate the area:
[tex]\[
A \approx \sqrt{10251.5} \approx 102.3
\][/tex]
3. Select the Closest Answer:
Comparing the calculated area with the options provided:
- a. 99.1 units²
- b. 100.5 units²
- c. 98.7 units²
- d. 102.3 units²
The calculated area, 102.3, is closest to option D.
So, the best choice is:
D. 102.3 units²
1. Calculate the Semi-perimeter (s):
The semi-perimeter [tex]\( s \)[/tex] is half of the sum of the sides of the triangle.
[tex]\[
s = \frac{a + b + c}{2} = \frac{25 + 13 + 17}{2} = \frac{55}{2} = 27.5
\][/tex]
2. Apply Heron's Formula:
Heron's formula states that the area [tex]\( A \)[/tex] of a triangle with semi-perimeter [tex]\( s \)[/tex] and sides [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] is:
[tex]\[
A = \sqrt{s(s - a)(s - b)(s - c)}
\][/tex]
Substituting the values into the formula:
[tex]\[
A = \sqrt{27.5 \times (27.5 - 25) \times (27.5 - 13) \times (27.5 - 17)}
\][/tex]
[tex]\[
A = \sqrt{27.5 \times 2.5 \times 14.5 \times 10.5}
\][/tex]
Calculate the area:
[tex]\[
A \approx \sqrt{10251.5} \approx 102.3
\][/tex]
3. Select the Closest Answer:
Comparing the calculated area with the options provided:
- a. 99.1 units²
- b. 100.5 units²
- c. 98.7 units²
- d. 102.3 units²
The calculated area, 102.3, is closest to option D.
So, the best choice is:
D. 102.3 units²
Thanks for taking the time to read What is the area of a triangle with tex a 25 tex tex b 13 tex and tex c 17 tex A 99 1 units. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
