Question

what is the missing length?

Explanation:

Step1: Identify the right - angled triangle

The rectangle's diagonal divides it into two right - angled triangles. The two sides of the right - angled triangle are 30 yards and 40 yards.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 30$, $b = 40$, and $c$ is the hypotenuse (the missing length). So $c=\sqrt{30^{2}+40^{2}}$.

Step3: Calculate the squares

$30^{2}=900$ and $40^{2}=1600$. Then $30^{2}+40^{2}=900 + 1600=2500$.

Step4: Find the square root

$c=\sqrt{2500}=50$.

Answer:

50