Question

If the hypotenuse of a right angle triangle is 6m more than twice the shortest side and third side is 2m less than the hypotenuse. Find the sides of the triangle

Answer 1

Let the shortest side be x

Then hypotenuse = 2x+6

Third side= 2x+6-2= 2x+4

Now pythogerean formula:
${h}^{2} = {b}^{2} + {p}^{2} \\ {(2x + 6)}^{2} = {x}^{2} + {(2x + 4)}^{2} \\ 4 {x}^{2} + 36 = {x}^{2} + 4 {x}^{2} + 16 \\ {x}^{2} + 4 {x}^{2} - 4 {x}^{2} = 36 - 16 \\ {x}^{2} = 20 \\ x = \sqrt{20} \\ x = 4.47m$

Hypotenuse = 2x+6

= 2*4.47+6= 14.94m

Third side = 2x+4

= 2*4.47+4= 12.94m

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Answer 2

Answer:

• 10 m , 26 m , 24 m

Step-by-step explanation:

Given

• Hypotenuse of a right angle triangle is 6m more than twice the shortest side.
• Third side is 2m less than the hypotenuse.

To find

• Sides of the triangle.

Solution

(Let the shortest side be x m)

Then hypotenuse:

• 2x + 6 m

Third side:

• 2x + 4 m

By Pythagoras theorem:

• (2x + 6)² = x² + (2x + 4)²
• 4x² + 24x + 36 = x² + 4x² + 16x + 16
• x² - 8x - 20 = 0
• (x - 10) (x + 2) = 0
• x = 10 or x = -2

x can't be negative, so value of x is 10

Hence, the sides of triangle are:

• 10 m , 26 m , 24 m