+0

# a rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of the park. After heavy rain, two adjacent

0
330
1

a rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of the park. After heavy rain, two adjacent sides are too muddy to run along, so he runs a triangular path along the other two sides and the diagonal. Danny does 5 circuits of this path for training. Show that danny runs about 970 metres less than his usual training session.

Guest Jun 4, 2015

#1
+26402
+10

Usual training distance = 5*2*(260 + 480) m

Diagonal distance = √(2602 + 4802) m

Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m

Difference between these:

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{260}}{\mathtt{\,\small\textbf+\,}}{\mathtt{480}}\right){\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}\left({\mathtt{260}}{\mathtt{\,\small\textbf+\,}}{\mathtt{480}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{260}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{480}}}^{{\mathtt{2}}}}}\right) = {\mathtt{970.531\: \!187\: \!208\: \!763\: \!874\: \!4}}$$

difference = 971 m to nearest metre

.

Alan  Jun 4, 2015
Sort:

#1
+26402
+10

Usual training distance = 5*2*(260 + 480) m

Diagonal distance = √(2602 + 4802) m

Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m

Difference between these:

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{260}}{\mathtt{\,\small\textbf+\,}}{\mathtt{480}}\right){\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}\left({\mathtt{260}}{\mathtt{\,\small\textbf+\,}}{\mathtt{480}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{260}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{480}}}^{{\mathtt{2}}}}}\right) = {\mathtt{970.531\: \!187\: \!208\: \!763\: \!874\: \!4}}$$

difference = 971 m to nearest metre

.

Alan  Jun 4, 2015

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details