Question

the length of two sides of a right triangle are equal. the square of the hypotenuse 800 cm2 find the length of each side​

Answer 1

Answer:

20cm

Step-by-step explanation:

x^2+x^2=800cm

x^2=800/2

x^2=400

x= root of 400

=20cm

Answer 2

Given

• Length of two sides of a right angled triangle are equal.
• The square of the hypotenuse = 800 cm²

To find

• Length of each side.

Solution

Let the two equal angles be x cm each.

By using pythagoras theorem,

⟼ (x)² + (x)² = 800

⟼ x² + x² = 800

⟼ 2x² = 800

⟼ x² = 800/2

⟼ x² = 400

⟼ x = √400

⟼ x = √20 × 20

⟼ x = ± 20 Reject - ve

⟼ x = 20 cm

The value of x = 20 cm

★ The length of each equal side = 20 cm.

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Now, finding the length of the hypotenuse :-

By using pythagoras theorem,

⟼ (H)² = (20)² + (20)²

⟼ (H)² = 400 + 400

⟼ (H)² = 800

⟼ H = √800

⟼ H = 28.28 cm

★ Hypotenuse = 28.28 cm

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Let's verify :-

If the sum of the squares of the two sides is equal to the square of the third side. Then the values are right.

By using pythagoras theorem,

⟼ H² = P² + B²

where,

• H = hypotenuse (longest side)
• P = perpendicular
• B = base

Hypotenuse = 28.28 cm

Taking Lhs,

⟼ (28.28)²

⟼ 800 cm²

Taking Rhs,

⟼ (20)² + (20)²

⟼ 400 + 400

⟼ 800

Lhs = Rhs

Hence, verified.