Question

a triangular pyramid is formed from three right triangles as shown below. use the information given in the figure to find the length rt. if applicable, round your answer to the nearest whole number. the lengths on the figure are not drawn accurately.

Explanation:

Step1: Find QT using Pythagoras (if needed, but first find ST)

Wait, actually, let's look at triangle QTS? No, first, let's see the right triangles. Let's assume RT is perpendicular to the base, so triangle RTS and RTQ are right triangles? Wait, the figure has QT = 5, QS = 13? Wait, no, QS is 13? Wait, the side QS is 13? Wait, no, the side from Q to S is 13, and from S to R is 37, and QT is 5. Wait, maybe first find ST. Since QS is 13, QT is 5, so in triangle QTS (right triangle? Wait, the dashed lines: QT is 5, QS is 13, so ST can be found by Pythagoras. Wait, QT is 5, QS is 13, so ST = $\sqrt{13^2 - 5^2}$? Wait, no, if QT is 5, and QS is 13, and T is a right angle? Wait, maybe triangle QTS is right-angled at T? So QT = 5, QS = 13, so ST = $\sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12$. Then, in triangle RTS, which is right-angled at T (since RT is perpendicular to the base), RS = 37, ST = 12, so RT can be found by Pythagoras: RT = $\sqrt{RS^2 - ST^2} = \sqrt{37^2 - 12^2}$.

Step2: Calculate RT

First, compute $37^2 = 1369$ and $12^2 = 144$. Then, $1369 - 144 = 1225$. Then, $\sqrt{1225} = 35$.

Answer:

35