Question

solve for x to the nearest tenth.

Explanation:

Step1: Find the length of the diagonal of the rectangle

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for the right - angled triangle in the rectangle with sides 3 and 5. Let the diagonal of the rectangle be $d$.
$d=\sqrt{3^{2}+5^{2}}=\sqrt{9 + 25}=\sqrt{34}$

Step2: Use the Pythagorean theorem for the large right - angled triangle

The large right - angled triangle has sides $\sqrt{34}$ and 9, and the hypotenuse is $x$.
By the Pythagorean theorem $x=\sqrt{(\sqrt{34})^{2}+9^{2}}=\sqrt{34 + 81}=\sqrt{115}$

Step3: Calculate the value of $x$ to the nearest tenth

$\sqrt{115}\approx10.7$

Answer:

$10.7$