Question

find the value of x in the triangle shown below. choose 1 answer. x = √28 x = √56 4 of 7

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $a = 12$, $b = 16$, and $c=x$. So, $x^{2}=12^{2}+16^{2}$.

Step2: Calculate the squares

$12^{2}=144$ and $16^{2}=256$. Then $x^{2}=144 + 256$.

Step3: Add the values

$144+256 = 400$. So, $x^{2}=400$.

Step4: Solve for $x$

Taking the square - root of both sides, $x=\sqrt{400}=20$. But if we consider the options in terms of square - roots, $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=\sqrt{56\times\frac{400}{56}}=\sqrt{56\times\frac{100}{14}}
eq\sqrt{28}$. Also, $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20=\sqrt{400}=\sqrt{56\times\frac{400}{56}}
eq\sqrt{28}$.
The correct way using the Pythagorean theorem: $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400} = 20$. If we rewrite it in square - root form without simplifying completely: $x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}=\sqrt{56\times\frac{400}{56}}=\sqrt{56\times\frac{100}{14}}$. But if we just calculate directly from the theorem $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$. In terms of the given options, we know that $x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}$.
We know that $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}$. Since $12^{2}+16^{2}=144 + 256=400$, $x=\sqrt{400}$.

Answer:

$x = 20$ (It seems there is an error in the provided options as the correct value of $x$ from the Pythagorean theorem calculation for the right - triangle with legs 12 and 16 is 20, not in the form of $\sqrt{56}$ or $\sqrt{28}$. If we assume we must choose from the given options based on the Pythagorean calculation process, we note that $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}$. But if we follow the steps strictly, the value calculated is 20. If we consider the form of square - roots in the options, we re - calculate $x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}$. The closest in terms of the Pythagorean calculation process: $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}$. There is a mismatch between the correct value and the options provided, but the correct value from the Pythagorean theorem for this right - triangle is $x = 20$).

It should be noted that if we assume the options are mis - written and we just calculate $x$ using the Pythagorean theorem for a right - triangle with legs 12 and 16, we get $x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$. If we were to force a choice from the given options based on the calculation process, we would note that the calculation $x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}$ does not match $\sqrt{28}$, and we can show the relationship with $\sqrt{56}$ in the above steps, but the correct geometric calculation gives $x = 20$.