Question

This picture shows a proof of the Pythagorean theorem because (1 point) Responses The yellow triangles fill up the large squares just enough to have a small square in each figure. The yellow triangles fill up the large squares just enough to have a small square in each figure. The four yellow triangles are congruent in both large squares and the large squares are congruent, so c2=a2+b2 The four yellow triangles are congruent in both large squares and the large squares are congruent, so c squared is equal to A squared plus b squared a = b = c, so the Pythagorean theorem holds true. a = b = c, so the Pythagorean theorem holds true. a < b < c, so the Pythagorean theorem holds true.

Answer 1

Jimmy ran 40 meters West from home and then turned north to jog 15 meters. Jimmy ran 55 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?
A: 8 m
B: 912.5 m
C: 15 m
D: 42.7 m

Answer 2

The yellow triangles fill up the large squares just enough to have a small square in each figure.

Answer 3

To find the straight line distance Jimmy could have jogged, we can use the Pythagorean theorem.
The distance Jimmy ran West is 40 meters, and the distance he ran North is 15 meters. Therefore, the total distance he ran is the hypotenuse of a right triangle with sides of 40 and 15 meters.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 40^2 + 15^2
c^2 = 1600 + 225
c^2 = 1825
c ≈ √1825
c ≈ 42.7 meters

Therefore, the answer is D: 42.7 meters.