Answer:
QR = 15 cm
PQ = 20 cm
Step-by-step explanation:
Use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]
Find QR first since you know QP are SR.
[tex]a^{2} +b^{2} =c^{2}\\12^{2} +9^{2} =c^{2}\\144+81=c^2 \\225=c^2\\\sqrt{225} = \sqrt{c^2} \\c = 15[/tex]
QR = 15 cm
Now you can find PQ. First find the length of PR by adding PS and SR together.
16 + 9 = 25
[tex]a^{2} +b^{2} =c^{2}\\a^{2} +15^{2} =25^{2}\\a^{2} +225 =625\\a^{2} +225-225 =625-225\\\a^{2} = 400\\\sqrt{a^2} =\sqrt{400} \\a = 20[/tex]
PQ = 20 cm
