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:

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