The hypotenuse of right triangle is 116 meters long. The difference between the other two sides is 4 meters. Find the missing sides. Use exact values.

Longer side = 84 meters

Shorter side = 80 meters

Step-by-step explanation:

The hypotenuse is the longest side of the right angle triangle. Let x represent the length of the longer side of the triangle. The difference between the other two sides is 4 meters. It means that the length of the shorter side is x - 4

Applying Pythagoras theorem which is expressed as

Hypotenuse² = longer side² + shorter side²

Therefore,

116² = x² + (x - 4)²

13456 = x² + x² - 4x - 4x + 16

2x² - 8x + 16 - 13456 = 0

2x² - 8x - 13440 = 0

Dividing through by 2, it becomes

x² - 4x - 6720

x² + 80x - 84x - 6720 = 0

x(x + 80) - 84(x + 80) = 0

x - 84 = 0 or x + 80 = 0

x = 84 or x = - 80

Since the length cannot be negative, then

x = 84

Length of shorter side is

84 - 4 = 80

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."