Question

find the value of x.
12
12
x = ?
round to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (both legs are 12 units). We can use the Pythagorean theorem, which states that for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 12\), \(b = 12\) and \(c=x\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 12\) and \(b = 12\) into the formula:
\(x^{2}=12^{2}+12^{2}\)
\(x^{2}=144 + 144\)
\(x^{2}=288\)

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{288}\). We know that \(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\approx12\times1.414 = 16.968\)

Step4: Round to the nearest tenth

Rounding \(16.968\) to the nearest tenth gives \(17.0\)

Answer:

\(17.0\)