The diagram shows right-angled triangles $SUT$ and $RQT$, with $Q,U,T$ collinear in that order

Question

The diagram shows right-angled triangles $SUT$ and $RQT$, with $Q,U,T$ collinear in that order and $R,S,T$ collinear in that order. Given $QU=5\text{ cm}$, $UT=3\text{ cm}$, $SU=4\text{ cm}$, and $\angle SUT=\angle RQT=90^\circ$, calculate the following.

Calculate

the length of $ST$,
the length of $QR$,
the area of Figure $QRSU$.

Source correction: disregard the printed $RS=5.4\text{ cm}$ label. It is incompatible with the other lengths and the two right angles. The geometry determines $RS=25/3\text{ cm}$; the earlier transcribed $8.3\text{ cm}$ is also unsuitable as an exact additional given.

Accepted Answer

(a) $5\text{ cm}$. (b) $32/3\text{ cm}\approx10.7\text{ cm}$. (c) $110/3\text{ cm}^2\approx36.7\text{ cm}^2$.

Pythagoras’ Theorem - Applications of Pythagoras’ Theorem

Pythagoras’ Theorem - Applications of Pythagoras’ Theorem

Solution:

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