Question

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

Explanation:

Step1: Apply Pythagorean theorem

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

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

\(40^{2}=1600\) and \(9^{2}=81\). 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:

41 units