Question

A block of land is in the shape of a right angle triangle with a perimeter of 150m and a hypotenuse of 65m. Determine the lengths of the other two sides.

Answer 1

lengths of the other two sides are: 60m and 25m

Explanation:

x^2 + (85 - x)^2 = 65^2

x^2 + x^2 - 170x + 7225 = 4225

2x^2 - 170x + 7225 = 4225

2x^2 - 170x + 3000 = 0

2 (x^2 - 85x + 1500) = 0

(x - 60)(x - 25) = 0

x = 60

x = 25

plug in to check if viable

a^2 + b^2 = c^2

60^2 + 25^2 = 65^2

3600 + 625 = 4225

4225 = 4225

Answer 2

D = 150m

x= length of sides

2x+65=150

2x=150-65

x=21.25

one side is 21.25m

the hypotenuse is 65m

with the pythagorean theorem we calculate the 3rd side

65²=21.25²+c²

c²=65²-21.25²

c=V3773.4375 about 61.43m

side dimensions 65m 21.25m 61.43m

Explanation: