Apply Given:
Longer hypotenuse = 8
Longer base = 2
Total base = x + 2
Let's solve for x.
To solve for x, apply Pythagorean theorem to first find the altitude:
[tex]\begin{gathered} h=\sqrt{8^2-2^2} \\ \\ h=\sqrt{64-4} \\ \\ h=\sqrt{60} \\ \end{gathered}[/tex]Now, to find the shorter base, we have:
(x + 5) - 2 = x + 5 - 2 = x + 3
Apply the Triangle Altitude formula:
[tex]\frac{2}{\sqrt{60}}=\frac{\sqrt{60}}{x+3}[/tex]Cross multiply:
[tex]\begin{gathered} 2(x+3)=\sqrt{60}*\sqrt{60} \\ \\ 2(x+3)=60 \\ \\ Apply\text{ distributive property:} \\ 2x+2(3)=60 \\ \\ 2x+6=60 \\ \\ Subtract\text{ 6 from both sides:} \\ 2x+6-6=60-6 \\ \\ 2x=54 \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}[/tex]Therefore, the value of x is 27.
• ANSWER:
x = 27