Question

the hypothnue of right triangle is 2 more than twice of one ofthe other side while the 3rd side is 13 more than half of the hypothnue find the length of all the side​

Answer 1

Step-by-step explanation:

Given :-

The hypothnue of right triangle is 2 more than twice of one ofthe other side while the 3rd side is 13 more than half of the hypotenuse.

To find :-

Find the length of all the sides ?

Solution :-

Let the one side of the right angled triangle be X units

Then the hypotenuse of the right angled triangle

= 2 more than twice of the one side of the triangle

= (2X+2) units

The length of the third side

= 13 more than half of the hypotenuse

= (2X+2)/2 + 13

=> 2(X+1)/2 + 13

=> X+1+13

=> (X+14) units

The lengths are X units , (2X+2) units , (X+14) units

We know that

By Pythagoras theorem

Hypotenuse^2 = 1st Side^2 + 2nd Side^2

=> (2X+2)^2 = X^2+(X+14)^2

=> (2X)^2+2(2X)(2)+2^2 = X^2+X^2+2(X)(14)+14^2

Since (a+b)^2 = a^2+2ab+b^2

=> 4X^2+8X+4 = 2X^2+28X+196

=> 4X^2+8X+4-2X^2-28X-196 = 0

=> 2X^2-20X-192 = 0

=> 2(X^2-10X-96) = 0

=> X^2-10X-96 = 0/2

=>X^2-10X-96 = 0

=> X^2+6X-16X-96 = 0

=> X(X+6) -16(X+6) = 0

=> (X+6)(X-16) = 0

=>X+6 = 0 or X-16 = 0

=> X = -6 or X = 16

X cannot be negative

X = 16 units

One side = 16 units

Hypotenuse = 2X+2

=> 2(16)+2

=> 32+2

=> 34 units

Third side = (34/2)+14

=> 17+13

=> 30 units

The measurements are 16 units ,34 units ,

30 units

Answer:-

The measurements of all the sides of the right angled triangle are 16 units , 34 units and

30 units

Used formulae:-

Pythagoras Theorem:-

In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other sides.