Question

19
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note: figure not drawn to scale.
for the right triangle shown, which expression represents the value of b?
a ( 70 - 40 )
b ( sqrt { ( 70 ) ( 40 ) } )
c ( sqrt { 70 + 40 } )
d ( sqrt { 70 ^ { 2 } - 40 ^ { 2 } } )

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 40\), \(c=70\), and we need to find \(b\). So \(b^{2}=c^{2}-a^{2}\).

Step2: Solve for \(b\)

If \(b^{2}=70^{2}-40^{2}\), then \(b=\sqrt{70^{2}-40^{2}}\) (taking the positive square root since \(b\) represents the length of a side of a triangle).

Answer:

D. \(\sqrt{70^{2}-40^{2}}\)