Answer:
Length = [tex]2\sqrt{58}[/tex]
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 [tex]A= \frac{1}{2} b * h[/tex]
We know that the breadth, or the base, b, is 6 cm.
Substitute the value of 6 for B
[tex]A = 1/2(6) * h[/tex]
What we need to do is find the length of the height, H. Therefore
[tex]42 = 1/2(6) * h[/tex]
[tex]42 = 3h[/tex]
Divide each side by 3 to isolate h
[tex]14 = h[/tex]
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.
[tex]a^2 + b^2 = c^2\\6^2 + 14^2 = c^2\\36 + 196 = c^2\\232 = c^2[/tex]
Take the square root of both sides to simplify c.
[tex]c= 2\sqrt{58}[/tex]
This is approximately equal to
[tex]15.232[/tex] cm's
