Question

One leg of a right triangle is 15 cm. Its hypotenuse is 20 cm. How long is the other leg?

​

Answer 1

Answer:

13

Step-by-step explanation:

Given that one leg of a right triangle is 15 cm and it's hypotenuse is 20 cm. We need to find out the other leg of the triangle.

Let's say that the triangle is ABC having sides AB, BC and AC & right angled at angle B (∠B = 90°). Also one leg, assume that leg as base.

We know that a triangle consists of three sides having base, perpendicular and hypotenuse. So, in ∆ABC base is BC having value 15, perpendicular is AB and hypotenuse is AC whose value is 20.

So,

(Hypotenuse)² = (Perpendicular)² + (Base)²

H² = P² + B²

Substitute the values,

→ (20)² = P² + (15)²

→ 400 = P² - 225

→ 400 - 225 = P²

→ 175 = P²

→ P = √175

→ P = 13.23

→ P = 13 (approx.)

Therefore, the other leg is 13 cm long.

Answer 2

Answer:

$5\sqrt{7}$

Step-by-step explanation:

Given data:

• One leg of a right triangle is $15cm$ , its hypotenuse is $20cm$

• As per the data given in the question, we need to find the other leg of the triangle.

• According to Pythogoras theorem

$Hypotenuse^{2} =height^{2} +base^{2}$

• On substituting the given values in the above formula, we get

$20^{2} =15^{2} +base^{2}$

$base^{2} =400-225$

$base^{2} =175$

base $=\sqrt{175}$

base$=\sqrt{25\times7}$

base$=5\sqrt{7}$

Hence, the length of the other leg of the right triangle is $5\sqrt{7}$.