The legs are related as 1: 3 to find the height drawn from the top of the right angle to the hypotenuse
The legs are related as 1: 3 to find the height drawn from the top of the right angle to the hypotenuse. If hypotenuse = 40.
Let’s find the lengths of the legs of this right-angled triangle.
Let’s denote by x the length of the smaller leg.
According to the condition of the problem, the legs of a given right-angled triangle are related as 1: 3, therefore, the length of the larger leg is 3x.
By the condition of the problem, the hypotenuse of this right-angled triangle is 40.
Using the Pythagorean theorem, we get the following equation:
x ^ 2 + (3x) ^ 2 = 40 ^ 2.
We solve the resulting equation:
x ^ 2 + 9x ^ 2 = 1600;
10x ^ 2 = 1600;
x ^ 2 = 1600/10;
x ^ 2 = 160;
x = √160;
x = 4√10.
We find a larger leg:
3x = 3 * 4√10 = 12√10.
Knowing both legs, we find the area S of this triangle:
S = 4√10 * 12√10 / 2 = 24 * 10 = 240.
Knowing the area of this triangle and the hypotenuse c, we find the height h drawn to the hypotenuse:
h = 2 * S / c = 2 * 240/40 = 2 * 6 = 12.
Answer: the length of the height drawn from the top of the right angle to the hypotenuse is 12.