Find the unknowns length x in the following figures: |
(a) |
(b) |
(c) |
(d) |
Answer:
(a) \[\Delta ABC\]is right-angled at B. ∴ By Pythagoras theorem, we have \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[{{x}^{2}}={{8}^{2}}+{{9}^{2}}\] \[{{x}^{2}}={{6}^{4}}+{{3}^{6}}\] \[x=\sqrt{100}=10\] (b) \[\Delta ABC\]is right-angled at B. ∴ By Pythagoras theorem, we have \[A{{C}^{2}}=A{{B}^{2}}+BC\] \[\Rightarrow {{x}^{2}}={{12}^{2}}+{{5}^{2}}\] \[\Rightarrow {{x}^{2}}=144+25\] \[\Rightarrow {{x}^{2}}=169\] \[\Rightarrow {{x}^{2}}=\sqrt{169}=13\] (c) DABC is right-angled at B. ∴ By Pythagoras theorem, we have \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[\Rightarrow {{x}^{2}}={{8}^{2}}+{{15}^{2}}\] \[\Rightarrow {{x}^{2}}=64+225\] \[\Rightarrow {{x}^{2}}=289\] \[x=\sqrt{289}=17\] (d) DABC is right-angled at B. ∴ By Pythagoras theorem, we have \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[\Rightarrow {{x}^{2}}={{24}^{2}}+{{7}^{2}}\] \[\Rightarrow {{x}^{2}}=576+49\] \[\Rightarrow {{x}^{2}}=625\] \[x=\sqrt{625}=25\]
You need to login to perform this action.
You will be redirected in
3 sec