Answer:
x = 21 units
Step-by-step explanation:
Given that,
Length of long leg of larger triangle = 72 units
Length of hypotenuse of larger triangle = 75 units
Length of shorter leg of larger triangle = ?
Length of longer leg of smaller triangle = 24 units
Length of shorter leg of smaller triangle = 7 units
Length of hypotenuse of smaller triangle = 25 units
Since, we know that,
(Hypotenuse)² = (Perpendicular)² + (Base)²
From the given condition it is clear that smaller triangle is right angle triangle. Since both triangle are similar. That means, larger triangle is also right angle triangle.
The above equation can be written as,
75² = 72² + (Base)²
(Base)² = 75² - 72²
(Base)² = 441
Base = 21
Therefore, The length of shorter leg of larger triangle is 21 units.
