Question

The length of one leg of a 45° − 45° − 90° triangle is 24. What is the perimeter of the triangle?

Answer 1

Answer:
second leg = 24 units
hypotenuse = 24√2 units
perimeter = 48 + 24√2 units

Explanation:
1- getting the other leg:
Since the triangle given is an isosceles triangle, this means that the two legs are equal in lengths.
We are given that one of the legs is 24 units, therefore, the other leg is also 24 units

2- getting the hypotenuse:
The given triangle is a right-angled triangle. We can use Pythagorean theorem to get the hypotenuse as follows:
(hypotenuse)² = (24)² + (24)²
(hypotenuse)² = 1152
hypotenuse = 24√2 units

3- getting the perimeter:
The perimeter of the triangle is the summation of its three sides.
In the given triangle, we have:
two legs = 24 units
hypotenuse = 24√2 units
Therefore:
perimeter = 24 + 24 + 24√2
perimeter = 48 + 24√2 units

Hope this helps :)