Question

The triangles are similar. What is the value of x? Enter your answer in the box. x = two right triangles. the larger triangle has a long leg of 72 units, a short leg labeled x, and a hypotenuse of 75 units. the smaller triangle has a long leg of 24 units, short leg of 7 units, and a hypotenuse of 25 units.

Answer 1

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.