Question

in a right angled triangle if sum of squares of the sides of the side making right angle is 400 then what is the length of hypotenuse.

Answer 1

Step-by-step explanation:

the answer is in the attachment

Answer 2

Given :

• Sum of squares of the sides making the right angle = 400 units

To find :

• Length of the Hypotenuse

Solution :

Here, we are given that the sum of the squares of base and perpendicular is 400 units. And we have to find the length of the Hypotenuse. For that we will use the pythagoras theorem.

Pythagoras thereom,

• H² = P² + B²

where,

• H = Hypotenuse (which is also the longest side of the traingle.)

• P = Perpendicular (side on which the angle of 90° is there.)

• B = Base of the triangle

we have,

• P² + B² = 400 units

Substituting the values in the pythagoras theorem,

$\\ \longrightarrow \quad \sf{H^2 = P^2 + B^2}$

$\\ \longrightarrow \quad \sf{H^2 = 400}$

Taking square root on both the sides.

$\\ \longrightarrow \quad \sf{H = \sqrt{400}}$

$\\ \longrightarrow \quad \sf{H = \sqrt{20 \times 20}}$

$\\ \longrightarrow \quad \sf{H = \pm \: \: 20}$

As we know that the side of triangle cannot be negative. So, the negative sign will get rejected.

$\\ \longrightarrow \quad \sf{H = \pm \: \: 20 \: \: Reject \: - ve}$

$\\ \longrightarrow \quad \sf{H = 20 }$

Therefore,

• Length of the Hypotenuse = 20 units

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Let's verify!

To verify our answer, find the square of hypotenuse. If it will be equal to the sum of the squares of perpendicular and the base. Then the value will be right.

H² = P² + B²

Finding the square of hypotenuse,

$\\ \longrightarrow \quad \sf{H = \big(20 \big) ^{2} }$

$\\ \longrightarrow \quad \sf{H = \big(20 \times 20 \big) }$

$\\ \longrightarrow \quad \sf{H = 400}$

Square of hypotenuse = 400 units

• H² = 400 units

The sum of the square of perpendicular and base = 400 units

• P² + B² = 400 units

Therefore,

• H² = P² + B²

Hence, verified.