Question

if the square of the hypotenuse of an isosceles right angle of an triangle is 128cm^2 find the length of each side​

Answer 1

Answer:

Base=Perpendicular= 8cm, Hypotenuse=8√2

Answer 2

AnswEr :

• The length of each equal side is 8 cm.

Given :

• The triangle formed is isosceles.

• Side (hypotenuse square) = 128 cm²

To find :

• Length of each side = ?

Solution :

Let us assume that the equal sides of the triangle be x.

Now,

By using Pythagoras theorem,

$\rm \dashrightarrow \ \ \ (H)^2 = (B)^2 + (P)^2$

$\rm \dashrightarrow \ \ \ 128 = x^2 + x^2$

$\rm \dashrightarrow \ \ \ 128 = 2x^2$

$\rm \dashrightarrow \ \ \ \dfrac{128}{2} = x^2$

$\rm \dashrightarrow \ \ \ x^2 = 64$

$\rm \dashrightarrow \ \ \ { \underline{ \boxed{ \rm{ \orange{x = 8 \ cm}}}}} \ \bigstar$

Therefore, the length of each equal side is 8 cm.

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★ Additional Information :

• Pythagoras theorem states that,

In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides !!

• Formula of Pythagoras theorem is,

$\dag \large \ { \boxed{ \rm{a^2 + b^2 = c^2}}}$

• a = side of right triangle .

• b = side of right triangle.

• c = hypotenuse .

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