![\tt Step-by-step~explanation:](https://img.qammunity.org/2021/formulas/mathematics/middle-school/1yvv69zlhkbxhn4v3cihgxbj4z92s81wn4.png)
![\tt Area:](https://img.qammunity.org/2021/formulas/mathematics/high-school/xehroqhl1hab2mobd778j19jrgzjbc9v4g.png)
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://img.qammunity.org/2021/formulas/mathematics/high-school/waxdjvscox5n0gknpn0e062idremmyjtg9.png)
![\tt Perimeter:](https://img.qammunity.org/2021/formulas/mathematics/high-school/podkwzhvpx7ogr7nr1ztsozai3y02bo8im.png)
![\tt Step~1:](https://img.qammunity.org/2021/formulas/mathematics/high-school/td6u35j3gyzkyxq2z12ex68fup5boe9d1z.png)
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=√(149)\\\sqrt{149](https://img.qammunity.org/2021/formulas/mathematics/high-school/qhsp8am7rcpgg4c0tkab0aq24ltn4i3ayc.png)
We cannot simplify √149, so we either leave it, or round it.
![\tt √(149)\\12.2066](https://img.qammunity.org/2021/formulas/mathematics/high-school/8fetse0juytn2a1mfoszjf87nwjez0at92.png)
This is rounded to the nearest 10,000.
![\tt Step~2:](https://img.qammunity.org/2021/formulas/mathematics/high-school/42ystigthi5jraeckxqu1502a0bp41zkf4.png)
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+√(149)=17+√(149)=P\\Rounded~to~the~nearest~1,000th:~29.207=P](https://img.qammunity.org/2021/formulas/mathematics/high-school/7p74o3zs0dsja825ctlxaobwq9c5nlfle2.png)
![\large\boxed{\tt Our~final~answer: ~A=35,~P=17+√(149)}](https://img.qammunity.org/2021/formulas/mathematics/high-school/qtr7cizsk73vtklbz7p1ejixjhlyh3jj3t.png)