Question

question 10 of 10
what is the length of (overline{ef}) in the right triangle below?

a. 24
b. 1296
c. 585
d. (sqrt{576})
e. 36
f. 54

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(DE^{2}=DF^{2}+EF^{2}\). Let \(EF = x\), \(DE = 39\), \(DF=15\). Then \(39^{2}=15^{2}+x^{2}\).

Step2: Rearrange the formula

\(x^{2}=39^{2}-15^{2}\). Using the difference of squares \(a^{2}-b^{2}=(a + b)(a - b)\), here \(a = 39\), \(b = 15\). So \(x^{2}=(39 + 15)(39 - 15)=(54)(24)=1296\).

Step3: Solve for \(x\)

Take the square root of both sides. \(x=\sqrt{1296}\). Since \(36\times36 = 1296\), \(x = 36\).

Answer:

E. 36