Question

1. find the unknown side of the triangle below (round to the nearest tenth). 25 cm x 10 cm 18 cm 22.9 cm 21.2 cm 26.9 cm

Explanation:

Step1: Identify triangle type

It's a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). In this triangle, the hypotenuse \(c = 25\space cm\), one leg \(a = 10\space cm\), and the other leg is \(x\) (the unknown side). We can re - arrange the formula to solve for \(x\): \(x=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute values

Substitute \(c = 25\) and \(a = 10\) into the formula. So \(x=\sqrt{25^{2}-10^{2}}=\sqrt{625 - 100}=\sqrt{525}\)

Step3: Calculate the square root

\(\sqrt{525}\approx22.9\space cm\) (rounded to the nearest tenth)

Answer:

22.9 cm (corresponding to the option "22.9 cm")