Question

You don’t have to explain everything just give me the answer as quick as possible it’s in the screenshot

Answer 1

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:

$\begin{gathered} h=\sqrt{8^2-2^2} \\ \\ h=\sqrt{64-4} \\ \\ h=\sqrt{60} \\ \end{gathered}$

Now, to find the shorter base, we have:

(x + 5) - 2 = x + 5 - 2 = x + 3

Apply the Triangle Altitude formula:

$\frac{2}{\sqrt{60}}=\frac{\sqrt{60}}{x+3}$

Cross multiply:

$\begin{gathered} 2(x+3)=\sqrt{60}*\sqrt{60} \\ \\ 2(x+3)=60 \\ \\ Apply\text{ distributive property:} \\ 2x+2(3)=60 \\ \\ 2x+6=60 \\ \\ Subtract\text{ 6 from both sides:} \\ 2x+6-6=60-6 \\ \\ 2x=54 \end{gathered}$

Divide both sides by 2:

$\begin{gathered} \frac{2x}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}$

Therefore, the value of x is 27.

• ANSWER:

x = 27