Answer:
Length = ![2\sqrt{58}](https://tex.z-dn.net/?f=2%5Csqrt%7B58%7D)
Explanation:
The width of the triangle is 6 cm. We are given the area. Lets work through this step by step.
First of all, the area of a triangle is ![A= \frac{1}{2} b * h](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%20b%20%2A%20h)
We know that the breadth, or the base, b, is 6 cm.
Substitute the value of 6 for B
![A = 1/2(6) * h](https://tex.z-dn.net/?f=A%20%3D%201%2F2%286%29%20%2A%20h)
What we need to do is find the length of the height, H. Therefore
![42 = 1/2(6) * h](https://tex.z-dn.net/?f=42%20%3D%201%2F2%286%29%20%2A%20h)
![42 = 3h](https://tex.z-dn.net/?f=42%20%3D%203h)
Divide each side by 3 to isolate h
![14 = h](https://tex.z-dn.net/?f=14%20%3D%20h)
The height is 14.
In order to determine the length, just substitute the values of 6 and 14 for a^2 and b^2 in the pythagorean theorem.
![a^2 + b^2 = c^2\\6^2 + 14^2 = c^2\\36 + 196 = c^2\\232 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%5C%5C6%5E2%20%2B%2014%5E2%20%3D%20c%5E2%5C%5C36%20%2B%20196%20%3D%20c%5E2%5C%5C232%20%3D%20c%5E2)
Take the square root of both sides to simplify c.
![c= 2\sqrt{58}](https://tex.z-dn.net/?f=c%3D%202%5Csqrt%7B58%7D)
This is approximately equal to
cm's