What is the area of a rectangle with a hypotenuse of 26 cm, one of the legs of which is 24 cm?

The area of ​​a right triangle can be found using the formula:
S = 1/2 * a * b,
where a and b are legs.
Since, according to the condition, the lengths of the hypotenuse of a right-angled triangle and one of the legs are given, then in order to find the area of ​​the triangle, you need to find the length of the second leg.
To find the length of the unknown leg, we use the Pythagorean theorem:
a ^ 2 + b ^ 2 = c ^ 2,
where a and b are the lengths of the legs of a right triangle, c is the hypotenuse of a right triangle.
Let’s substitute the data on the value condition into the formula:
a ^ 2 + 24 ^ 2 = 26 ^ 2.
Let’s solve the resulting equation:
a ^ 2 + 576 = 676;
a ^ 2 = 676 – 576;
a ^ 2 = 100;
a = √100;
a = 10 cm.
Find the area of ​​the triangle:
S = 1/2 * 10 * 24 = (1 * 10 * 24) / 2 = 240/2 = 120 (cm ^ 2.
Answer: S = 120 (cm ^ 2).