Question

The measure of hypotenuse of a isosceles right angle triangle is 3√2, what is the measure of its equal side?
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Answer 1

★ Given That :

• » The measure of hypotenuse of a isosceles right angle triangle is 3√2.

★ Need To FinD :

• » Measure of its equal side ?

⌬ Concept UseD Here :

➲ Isosceles triangle two sides are equal to each other so we can easily assume that Let the two equal sides of isosceles triangle be ‘x’. [ Assumption ]

➲ So let start solving it further to find the measurements of equal sides!

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✇ Applying Pythagoras Theorum :

• ➣ (H) ² = (B) ² + (P) ²

❒ Putting Values in Formula :

• ⇒ (3√2)² = (x)² + (x)²
• ⇒ 9 × 2 = x² + x²
• ⇒ 18 = 2x²
• ⇒ 18 / 2 = x²
• ⇒ 9 = x²
• ⇒ √9 = x
• ⇒ Value of ‘x’ = 3 cm

◆ Therefore :

• ➮ Measure of equal sides Isosceles ∆ is 3 cm

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Answer 2

ANSWER:

Given:

• Hypotenuse of an isosceles right angle triangle = 3√2

To Find:

• Measure of the equal sides.

Solution:

We are given that,

⇒ Hypotenuse = 3√2 units

Let the measure of equal sides be x units.

We know that, by Pythagoras Theorem,

⇒ (Hypotenuse)² = (Base)² + (Height)²

Here, measure of Hypotenuse is 3√2 and that of Height and Base is x.

So,

⇒ (Hypotenuse)² = (Base)² + (Height)²

⇒ (3√2)² = (x)² + (x)²

⇒ (√18)² = 2x²

⇒ 18 = 2x²

⇒ 2x² = 18

⇒ x² = 18/2

⇒ x² = 9

Taking square root both sides,

⇒ x = ±3

As, length can not be negative, value of x is 3.

Therefore, the measure of length of the equal sides is 3units.

Formula Used:

• (Hypotenuse)² = (Base)² + (Height)²