Question

Please help! I really don’t get this and it would be really helpful if you can give me the answers for these.

Answer 1

Answer:

for the first triangle, the length of the third side is 37 units

for the second triangle, the length of the third side is 29 units

Explanation:

Given the triangles in the attached image.

Let us apply the Pythagorean theorem to solve for the third side.

$\begin{gathered} c^2=a^2+b^2 \\ c=\sqrt{a^2+b^2} \end{gathered}$

For the first triangle;

$\begin{gathered} a=12 \\ b=35 \end{gathered}$

substituting the values;

$\begin{gathered} c=\sqrt[]{12^2+35^2} \\ c=\sqrt[]{1369} \\ c=37 \end{gathered}$

For the second triangle;

$\begin{gathered} a=20 \\ b=21 \end{gathered}$

substituting the values;

$\begin{gathered} c=\sqrt[]{20^2+21^2} \\ c=\sqrt[]{841} \\ c=29 \end{gathered}$

Therefore, for the first triangle, the length of the third side is 37 units

for the second triangle, the length of the third side is 29 units