Pythagoras' Theorem practice questions

• $\text{Since }\triangle TUV\text{ is isosceles and } TH \perp UV, H \text{ is the midpoint of } UV$
• $UH = \frac{UV}{2} = \frac{30}{2} = 15$ cm
• $\text{In }\triangle TUH\text{, } \angle THU = 90°$
• $TU^2 = TH^2 + UH^2 \quad \scriptsize\textit{Pythagoras' theorem}$
• $17^2 = TH^2 + 15^2$
• $TH^2 = 17^2 - 15^2$
• $TH^2 = 289 - 225$
• $TH^2 = 64$

Answer: $8$

• $\text{Vertical difference} = 28 - 12$
• $= 16$ m
• $\text{The cable forms the hypotenuse of a right-angled triangle with legs 16 m and 30 m.}$
• $\text{Let the cable length} = c$ m
• $c^2 = 16^2 + 30^2 \quad \scriptsize\textit{Pythagoras' theorem}$
• $c^2 = 256 + 900$
• $c^2 = 1156$
• $c = 34$ m

Answer: $34$

• $\text{Arrange the sides in order: } 10, 24, 26$
• $\text{The longest side is } MP = 26$ cm
• $MP^2 = 26^2$
• $= 676$
• $MN^2 + NP^2 = 10^2 + 24^2$
• $= 100 + 576$
• $= 676$
• $\text{Since } MP^2 = MN^2 + NP^2, \text{ }\triangle MNP\text{ is right-angled.} \quad \scriptsize\textit{converse of Pythagoras' theorem}$

Answer: $120$