Answer:
1. The measure of other leg is √(112) units. Therefore the correct option is 2.
2. The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples.
3. Therefore, the length of the hypotenuse is√(85).
4. Frank walks 19.31 blocks.
Step-by-step explanation:
1. The leg of a right triangle is 3 units and the hypotenuse is 11 units.
Using Pythagoras theorem:
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
[tex](11)^2=(3)^2+(leg_2)^2[/tex]
[tex]121=9+(leg_2)^2[/tex]
[tex]121-9=(leg_2)^2[/tex]
[tex]112=(leg_2)^2[/tex]
Taking square root both the sides.
[tex]\sqrt{112}=leg_2[/tex]
The measure of other leg is √(112) units. Therefore the correct option is 2.
2. According to the Pythagorean Theorem, the sum of squares of two legs of a right angled triangle is equal to the sum of square of its hypotenuse.
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
The set of numbers is called Pythagorean triples if the sum of squares of two small numbers equal to the square of larger number.
Check the set 3,4,5.
[tex](5)^2=(3)^2+(4)^2[/tex]
[tex]25=9+16[/tex]
[tex]25=25[/tex]
LHS=RHS, therefore the the set 3,4,5 is a Pythagorean triples.
Check the set 8,15,17.
[tex](17)^2=(8)^2+(15)^2[/tex]
[tex]289=64+225[/tex]
[tex]289=289[/tex]
LHS=RHS, therefore the the set 8,15,17 is a Pythagorean triples.
3.
The legs of a right triangle are 6 units and 7 units.
Using Pythagorean Theorem,
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
[tex](hypotenuse)^2=(6)^2+(7)^2[/tex]
[tex](hypotenuse)^2=36+49[/tex]
[tex](hypotenuse)^2=85[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{85}[/tex]
Therefore, the length of the hypotenuse is√(85).
4. From the given figure it is clear that the distance between Derek's and Evan's house is 8 blocks. The distance between Frank's and Evan's house is 8 blocks.
Using Pythagoras theorem the distance between Derek's and Frank's house is
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
[tex](hypotenuse)^2=(8)^2+(8)^2[/tex]
[tex](hypotenuse)^2=64+64[/tex]
Taking square root both the sides.
[tex](hypotenuse)=\sqrt{128}=11.31[/tex]
The distance between Derek's and Frank's house is 11.31 blocks.
It is given that frank walk from his house to derek's house, then on to Evan's house along the path shown. So the total distance covered by him is
[tex]D=11.31+8=19.31[/tex]
Therefore Frank walks 19.31 blocks.
