Question

a rectangle has a width of 9 units and a length of 40 units. what is the length of a diagonal?
31 units
39 units
41 units
49 units

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, the length \(l = 40\), width \(w=9\), and diagonal \(d\) form a right - triangle. By the Pythagorean theorem \(d^{2}=l^{2}+w^{2}\).
So \(d^{2}=40^{2}+9^{2}\).

Step2: Calculate \(l^{2}+w^{2}\)

\(40^{2}=1600\), \(9^{2} = 81\). Then \(d^{2}=1600 + 81=1681\).

Step3: Find \(d\)

Take the square root of \(d^{2}\). Since \(d>0\), \(d=\sqrt{1681}\). And \(\sqrt{1681}=41\).

Answer:

C. 41 units