Question

In an isosceles right triangle, the length of one leg can be represented by the expression 2x-3, and the length of the other leg can be represented by the expression 5x-21. What is the length of the triangle's hypotenuse, in simplest radical form?

Answer 1

The length of the hypotenuse is √2

Explanation:

The diagram of the right angle triangle with its dimensions is attached in the photo. In an isosceles triangle, two sides and two angles are equal. This means that from our diagram, the opposite side and the adjacent side is equal. The two equal angles are 45 degrees each. Therefore,

2x - 3 = 5x - 21

Collecting like terms,

2x - 5x = -21 + 3x

-3x = -18

x = -18/-3 = 6

The opposite side = 5x - 21 = 5×6 -21

= 30-21 = 9

The adjacent side = 2x - 3 = 2×6 -3

= 12-3 = 9

Applying Pythagoras theorem,

Hypothenuse ^2 = adjacent ^2 + opposite ^2

Hypothenuse ^2 = 1^2 + 1^2

Hypothenuse ^2 = 1 + 1 = 2

Hypothenuse = √2