Question

1. what is the area of the square that can be drawn on side c of each triangle? a) b) 13 mm 5 mm c

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 5\) mm, \(b=c\) (wait, no, the hypotenuse is 13 mm, one leg is 5 mm, and the other leg is \(c\)). Wait, correct: in a right - triangle, \(c\) (the leg we need) and 5 mm are the legs, 13 mm is the hypotenuse. So \(c^{2}+5^{2}=13^{2}\), we need to find \(c^{2}\) (since the area of the square on side \(c\) is \(c^{2}\)).

Step2: Rearrange the Pythagorean theorem

We know that for a right - triangle with legs \(a\), \(b\) and hypotenuse \(h\), \(a^{2}+b^{2}=h^{2}\). Here, let \(a = c\), \(b = 5\), \(h=13\). So \(c^{2}=h^{2}-b^{2}\)

Step3: Substitute the values

Substitute \(h = 13\) and \(b = 5\) into the formula. \(h^{2}=13^{2}=169\), \(b^{2}=5^{2}=25\). Then \(c^{2}=169 - 25\)

Step4: Calculate the result

\(169-25 = 144\)

Answer:

The area of the square drawn on side \(c\) is 144 square millimeters.