Question

find the value of x in the isosceles triangle shown below. choose 1 answer: a ( x = sqrt { 52 } ) b ( x = sqrt { 40 } ) c ( x = 20 ) d ( x = 7 )

Explanation:

Step1: Divide the base

Since it's an isosceles triangle, the perpendicular from the vertex to the base bisects the base. So each part of the base is $\frac{4}{2}=2$.

Step2: Apply Pythagorean theorem

In the right - triangle formed (with legs \(2\) and \(6\), and hypotenuse \(x\)), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 2\), \(b = 6\), \(c=x\)), we have \(x=\sqrt{2^{2}+6^{2}}\).
Calculate \(2^{2}+6^{2}=4 + 36=40\). So \(x=\sqrt{40}\).

Answer:

B. \(x = \sqrt{40}\)