Find the length of the hypotenuse given by 2x + 3 if the shorter sides of a right angled triangle are 2x and 5.

Expert Answers

You need to use Pythagorean Theorem that relates the three sides of right triangle, such that:

`a^2 = b^2 + c^2`

a represents the longest side of triangle, called hypotenuse

b,c represent the two smaller sides

Since the problem provides the hypotenuse `2x + 3` and the legs `2x` and 5, yields:

`(2x + 3)^2 = (2x)^2 + 5^2`

Expanding the binomial to the left side, yields:

`4x^2 + 12x + 9 = 4x^2 + 25`

Reducing duplicate terms yields:

`12x = 25 - 9 => 12x = 16 => 3x = 4 => x = 4/3`

You may evaluate the length of hypotenuse `a` , substituting `4/3` for `x` , such that:

`a = 2x + 3 => a = 2*(4/3) + 3 => a = 8/3 + 3 => a = 17/3`

Hence, evaluating the length of hypotenuse, under the given conditions, yields `a = 17/3.`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Approved by eNotes Editorial Team