Question

in a right triangle, the hypothenuse is 10cm more than the shortest side. if third side is 6cm less than the hypotenuse, find the sides of triangle.​

Answer 1

let the first side be x

second side be x+10

third side be x+10-6= x+4

now comparing all sides sum=180

x+x+10+x+4=180

3x+14=180

3x=180-14

3x=166

x=166/3

x=55.3

now x=55.3

x+10=65.3

x+4=59.3

Answer 2

Answer:

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Step-by-step explanation:

The hypothenuse of a right angle triangle is 6 mts more than the twice of the shortest side and the third side is 2 mts less than the hypothenuse.

To find:

Find the sides of the triangle ?

Solution:

Let the length of the shortest side of a right angled triangle be X metres

The length of the hypotenuse = 6 metres more than the twice of the shortest side.

=>Hypotenuse = (2X+6) metres

Length of the third side = 2 metres less than the Hypotenuse

=>Third side = (2X+6-2) metres

Third side = (2X+4) metres =

We know that Pythagoras Theorem

"In a right angled triangle, The square of the Hypotenuse is equal to the sum of the squares of the other two sides ".

$⟹ {(2x + 6)}^{2} = {x}^{2} + {(2x + 4)}^{2}$

$⟹ {(2x)}^{2} + 2(2x)(6) + {(6)}^{2} = {x}^{2} + {(2x)}^{2} + (2x)(4) + {4}^{2}$

$⟹ {4x}^{2} + 24x + 36 = {x}^{2} + {4x}^{2} + 16x + 16$

$⟹ {4x}^{2} + 24x + 36 = {5x}^{2} + 16x + 16$

$⟹ {5x}^{2} + 16x + 16 - {2x}^{2} - 24x - 36 = 0$

$⟹ {x}^{2} - 8x - 20 = 0$

$⟹ {x}^{2} + 2x - 10x - 20 = 0$

$⟹x(x + 2) - 10(x + 2) = 0$

$⟹(x + 2)(x - 10) = 0$

$⟹x + 2 = 0 \: \: or \: \: x - 10 = 0$

$⟹x = - 2 \: \: or \: \: x = 10$

X cannot be negative since the length of the side is always a positive

Therefore, X = 10 metres

The shortest side = 10 metres

Third side

= 2x + 4

= 2( 10) + 4

= 20 + 4

= 24 metres

Hypotenuse = 24 + 2 = 26 metres

Answer

The three sides of the given triangle are 10 metres , 24 metres and 26 metres.

Used formula:

• Used formula:Pythagoras Theorem:"In a right angled triangle, The square of the Hypotenuse is equal to the sum of the squares of the other two sides ".