[tex]\tt Step-by-step~explanation:[/tex]
[tex]\tt Area:[/tex]
To solve for the area of a triangle, we multiply the length and height, then divide that by two. L = 10. H = 7.
[tex]\tt 10*7=70\\70/2=35\\35=A[/tex]
[tex]\tt Perimeter:[/tex]
[tex]\tt Step~1:[/tex]
To solve for the perimeter, or edges, of the triangle, we need to use the Pythagorean Theorem: a² + b² = c² to solve for the third side. We already know two measures: 10 and 7. Now we need to square them, add them together to get c², then take the root of that number.
[tex]\tt 7^2=49\\10^2=100\\100+49=\sqrt{149}\\\sqrt{149[/tex]
We cannot simplify √149, so we either leave it, or round it.
[tex]\tt \sqrt{149}\\12.2066[/tex]
This is rounded to the nearest 10,000.
[tex]\tt Step~2:[/tex]
Now that we have the measure of the longest side, we can add all three sides together to get the perimeter of the triangle.
[tex]\tt 10+7+\sqrt{149}=17+\sqrt{149}=P\\Rounded~to~the~nearest~1,000th:~29.207=P[/tex]
[tex]\large\boxed{\tt Our~final~answer: ~A=35,~P=17+\sqrt{149}}[/tex]
