Question

the hypothenuse of a right angle triangle is 6 mts more than the twice of the shortest side.if the third side is 2 mts less than the hypothenuse. find the sides of the triangle​

Answer 1

Step-by-step explanation:

Given:-

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+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 -4X^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 number.

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:-

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 ".