Question

note: figure is not drawn to scale.
if ( k = 56 mathrm { cm } ) and ( l = 65 mathrm { cm } ), what is the length of ( j )?
a. ( 36 mathrm { cm } )
b. ( 86 mathrm { cm } )
c. ( 33 mathrm { cm } )
d. ( 39 mathrm { cm } )

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(j^{2}+k^{2}=l^{2}\), so \(j^{2}=l^{2}-k^{2}\).

Step2: Substitute values

Given \(k = 56\) and \(l = 65\), then \(j^{2}=65^{2}-56^{2}\).
Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(j^{2}=(65 + 56)(65 - 56)\).
\(j^{2}=(121)\times(9)\).
\(j^{2}=1089\).

Step3: Solve for \(j\)

Take the square root of both sides, \(j=\sqrt{1089}\).
\(j = 33\).

Answer:

C. 33 cm