Answer:
a = √85 and b = 2
Step-by-step explanation:
The quadrilateral is split into two right triangles. We can use Pythagorean Theorem to find the values of a and b. Pythagorean Theorem says that [tex]a^2 + b^2 = c^2[/tex],. In words, the squares of the shorter sides of a right triangle add up to the square of the hypotenuse.
Let's start by finding a. a is the hypotenuse of both triangles, and since we have the two other side lengths of the top triangle, we can plug the values into [tex]a^2 + b^2 = c^2[/tex] to find a.
[tex]6^2+7^2 = a^2\\85 = a^2\\\sqrt{85} =a[/tex]
Now that we have the length of a, we can plug the side lengths of the bottom triangle into the equation to find the length of b.
[tex]9^2+b^2=\sqrt{85} ^2\\81+b^2=85\\b^2=4\\b=2[/tex]
So, a = √85 and b = 2
