One leg of a right triangular piece of land has a length of 24 yards. they hypotenuse has a length of 74 yards. the other leg has a length of 10x yards. what is the value of x?

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c². 

Given 

One leg of a right triangular piece of land has a length of 24 yards. They hypotenuse has a length of 74 yards. The other leg has a length of 10x yards.

First leg (24 yards) would be α 

Second leg would be β

Hypotenuse (74 yards) would be c

Now we have points α β c.  

a² (24) + β² ( x ) = c² (74) 

Calculations 

c² = α² + β²

74² = 24²+ β² 

5476 = 576 + β² 

5476 - 576 = β²
 
4900 = β² 

→√4900 
 
β = 70 yards 

70 = 10x 

x = 70÷10 = 7 yards  

The second leg = 7 yards