Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find the value of x.

x=4

Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

step 2:-

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

289 = 4x^2 +9(x^2+2x+1)

finding factors  70 X 52 = 3640

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and

x=4 and

we can not choose negative value so x value is 4

Final - x = 4

verification:-

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

x = 4

Step-by-step explanation:

The length of two legs of a right angle triangle are 2x and 3(x+1).  

The length of longest side is 17 units. It means measure of hypotenuse is 17 units.

According to the pythagoras theorem,

On splitting the middle terms we get

Using zero product property we get

The value of x can not be a negaive number, because for negative value of x the value of 2x is negative and side can not be negative.

Therefore, the value of x is 4.