a triangle has sides f length xcm,(2x-1)cm and (2x+1)cm. If its perimeter is 40, state the size of the largest angle of the triangle giving reasons

Answer 1

P = x + 2 x - 1 + 2 x + 1 = 40

5 x = 40 Divide both sides by 5

x = 8 cm

2 x - 1 = 2 * 8 - 1 = 16 - 1 = 15 cm

2 x + 1 = 2 * 8 + 1 = 16 + 1 = 17 cm

Largest angle = 90° becouse your triangle is right triangle.

Use the Pythagorean theorem.

The square of the hypotenuse is equal to
the sum of the squares of the other two sides.

In this case:

17 ^ 2 = 15 ^ 2 + 8 ^ 2

289 = 225 + 64

So your triangle is right triangle.