Question

the screen on a handheld device has dimensions 7 cm by 5 cm, and a diagonal of length x cm. what is the value of x? round your answer to two decimal places.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle (the screen with length \(a = 7\) cm, width \(b = 5\) cm and diagonal \(x\)), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\). So, \(x^{2}=7^{2}+5^{2}\).

Step2: Calculate \(7^{2}+5^{2}\)

\(7^{2}=49\), \(5^{2}=25\). Then \(x^{2}=49 + 25=74\).

Step3: Solve for \(x\)

\(x=\sqrt{74}\approx8.60\) (rounded to two decimal places).

Answer:

\(8.60\)