Calculate the specified length for the given shape.

Cevap:A student cuts a piece of cardboard into a right triangle. The horizontal base measures

15

cm and the vertical height measures

20

cm. The length of the slanted side (hypotenuse) is 【25】 cm.

Cevap

Applying the Pythagorean theorem (

a^2 + b^2 = c^2

), we substitute the legs

a = 15

and

b = 20

. Squaring these gives

225

and

400

. Adding them yields

625

. Taking the square root of

625

gives the hypotenuse length of

25

cm. Alternatively, this can be recognized as a scaled

3-4-5

right triangle, where each side is multiplied by

5

(

3 \times 5 = 15

4 \times 5 = 20

, and

5 \times 5 = 25

Adım Adım Çözüm

Identify the known values in the Pythagorean theorem formula,

a^2 + b^2 = c^2

The legs are

a = 15

and

b = 20

. The hypotenuse

c

is unknown.

The Pythagorean theorem defines the relationship between the lengths of the two legs of a right triangle and its hypotenuse.

Substitute the leg values into the theorem and square them.

15^2 + 20^2 = 225 + 400 = 625

. Thus,

c^2 = 625

This isolates the square of the unknown hypotenuse (

c^2

) on one side of the equation.

Take the square root of both sides to find the hypotenuse.

c = \sqrt{625} = 25

The square root gives the actual length of the side rather than its squared value.

Anahtar Kavram

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs (

a^2 + b^2 = c^2

Soru

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