Twenty nine is the shortest leg of a right triangle whose other leg and hypotenuse are consecutive whole numbers. What is the sum of the lengths of the other two sides

Answers

The sum of the lengths of the other two sides of a right triangle will be 841.

We have,

The shortest leg of a right triangle = 29,

And,

According to the question,

The other leg and hypotenuse of a right triangle are consecutive whole numbers,

i.e.

Let,

Other leg = x,

And,

Hypotenuse = x+1,

So,

Now,

Using Pythagoras Theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

i.e.

H² = P² + B²

So,

Now Putting values,

i.e.

(x+1)² = x² + 29²

So,

On Solving we get,

x² + 1 + 2x = x² + 841

⇒

x² + 2x – x² = 841 – 1

We get,

2x = 840

So,

x = 420

I.e.

Other leg = 420,

So,

Hypotenuse = x+1 = 420 + 1 = 421,

Now,

The sum of the lengths of the other two sides of right triangle,

i.e.

Hypotenuse + Other leg = 420 + 421 = 841

Hence we can say that the sum of the lengths of the other two sides of a right triangle will be 841.

right trianglewill be 841.right triangle= 29,right triangleare consecutive whole numbers,right triangle,right trianglewill be 841.right trianglehere