Which statement is true about the lengths of the sides?

each side has a different length.

two sides have the same length, which is less than the length of the third side.

the three sides have the same length.

the sum of the lengths of two sides is equal to the length of the third side.

we know that

The triangle of the figure is an isosceles right triangle

so

The triangle has two equal sides and two equal angles

The two equal sides are called legs

The third side is called hypotenuse

Let

a,b-----> the legs of the triangle

c------> the hypotenuse

Applying the Pythagoras Theorem

so

------->

------->

Two sides have the same length, which is less  than the length of the third side

Statements

case A) Each side has a different length

The statement is False

Because, two length sides are equal

case B) Two sides have the same length, which is less than the length of the third side

The statement is True

See the procedure

case C) The three sides have the same length

The statement is False

Because, two length sides are equal and the third lenght side is different

case D) The sum of the lengths of two sides is equal to the length of the third side

The statement is False

Because, the sum of the squares of the legs equals the square of the hypotenuse

therefore

the answer is

Two sides have the same length, which is less than the length of the third side

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

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