decreases, what might happen to the distance of the shortcut? Justify your answe...

Questions

mightycapangpangan1 @mightycapangpangan1

October 2022 2 4 Report

A. Directions: Solve the given problems then answer the questions that follow
1. Juan is going to Nene's house to do a school project. Instead of walking two perpendicular streets to his
classmate's house, Juan will cut a diagonal path through the city plaza, Juan is 13 meters away from Nene's
street. The distance from the intersection of the two streets to Nene's house is 8 meters.
Questions:

a) How would you illustrate the problem?

b) How far will Juan travel along the shortcut?

c) How many meters will he save by taking the shortcut rather than walking along he sidewalks?

d) If one of the distance increases/decreases, what might happen to the distance of the shortcut? Justify your
answer.

e) What mathematical concepts did you use?

onlyakem

a) I will make a right triangle since the two streets are perpendicular to each other. The shortcut will be the hypothenuse since it is the shortest distance between two points. (Please refer to the attached image for the diagram. The diagram is part of the answer.)

b) He will have to walk 15 meters using the shortcut.

$a = 13 \: meters\\b = 8 \: meters$

$\small{c = \sqrt{ {a}^{2} + {b}^{2}} } \\ \small{ = \sqrt{ {13}^{2} + {8}^{2} }} \\ \small{= \sqrt{169 + 84}} \\ \small{ = \sqrt{233} } \\ \small{= 15.2643375225} \\ \small{c \approx15}$

c) He will save 6 meters if he travels through the shortcut.

$\small{distance \: saved = ( a + b) - c} \\ \small{= (13 + 8) - 15} \\ \small{= 21 - 15} \\ \small{= 6 \: meters}$

d) It will also increase since it is the hypothenuse of a right triangle.

If a = 15, then:

$\small{c = \sqrt{ {15}^{2} + {8}^{2} }} \\ \small{ = \sqrt{225 + 64}} \\ \small{ = \sqrt{289}} \\ \small{ c = 17}\\ \small{17>15}$

Similarly, if b = 10, then:

$\small{c = \sqrt{ {13}^{2} + {10}^{2} } } \\ \small{ = \sqrt{169 + 100}} \\ \small{ = \sqrt{269} } \\ \small{= 16.4012194669 }\\ \small{ c \approx16 \: meters}\\ \small{16>15}$

e) I used the Pythagorean Theorem which states that $c^{2}=a^{2}+b^{2}$ to calculate for the shortcut. I have also used the Perimeter of Triangle to calculate for the distance he will save. In order to compare, I used the concept of Comparing Inequalities.

jazelfaithmier thank you very much

litocardino thanks thankyou

miwpty thank you!

princessmicahtalaver thank you

Jamill19 Daniel Padilla is going to pay Kathryn Bernardo a visit. Instead of
walking two perpendicular streets to Kathryn's house, he decided to take the
straight path through an open ground. Daniel's house is 37 meters away from
Kathryn's house. The distance from the intersection of the perpendicular streets
to his house is 35 meters. How many meters will he save by taking the shortcut
rather than walking along the sidewalks?

Jamill19 pahelp nman dto lods. Hehe