![\tt Step-by-step~explanation:](https://tex.z-dn.net/?f=%5Ctt%20Step-by-step~explanation%3A)
![\tt Area:](https://tex.z-dn.net/?f=%5Ctt%20Area%3A)
To solve for the area of a triangle, we multiply the length and height, then divide that by two. L = 10. H = 7.
![\tt 10*7=70\\70/2=35\\35=A](https://tex.z-dn.net/?f=%5Ctt%2010%2A7%3D70%5C%5C70%2F2%3D35%5C%5C35%3DA)
![\tt Perimeter:](https://tex.z-dn.net/?f=%5Ctt%20Perimeter%3A)
![\tt Step~1:](https://tex.z-dn.net/?f=%5Ctt%20Step~1%3A)
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.
![\tt 7^2=49\\10^2=100\\100+49=\sqrt{149}\\\sqrt{149](https://tex.z-dn.net/?f=%5Ctt%207%5E2%3D49%5C%5C10%5E2%3D100%5C%5C100%2B49%3D%5Csqrt%7B149%7D%5C%5C%5Csqrt%7B149)
We cannot simplify √149, so we either leave it, or round it.
![\tt \sqrt{149}\\12.2066](https://tex.z-dn.net/?f=%5Ctt%20%5Csqrt%7B149%7D%5C%5C12.2066)
This is rounded to the nearest 10,000.
![\tt Step~2:](https://tex.z-dn.net/?f=%5Ctt%20Step~2%3A)
Now that we have the measure of the longest side, we can add all three sides together to get the perimeter of the triangle.
![\tt 10+7+\sqrt{149}=17+\sqrt{149}=P\\Rounded~to~the~nearest~1,000th:~29.207=P](https://tex.z-dn.net/?f=%5Ctt%2010%2B7%2B%5Csqrt%7B149%7D%3D17%2B%5Csqrt%7B149%7D%3DP%5C%5CRounded~to~the~nearest~1%2C000th%3A~29.207%3DP)
![\large\boxed{\tt Our~final~answer: ~A=35,~P=17+\sqrt{149}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctt%20Our~final~answer%3A%20~A%3D35%2C~P%3D17%2B%5Csqrt%7B149%7D%7D)