WILL GIVE BRAINLIST SOON AS I CAN is the second number 3?
2 answers:
Answer:
x = 2
Step-by-step explanation:
Using Pythagoras' identity on each of the 3 right triangles
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Outer right triangle
x² + z² = (9 + 4)² = 13² = 169, that is
x² + z² = 169 → (1)
Left right triangle
y² + 4² = x²
y² + 16 = x² ⇒ y² = x² - 16 → (2)
Right right triangle
z² = y² + 9²
z² = y² + 81 → (3)
Substitute (3) into (1)
x² + y² + 81 = 169 ← substitute (2) into here
x² + x² - 16 + 81 = 169
2x² + 65 = 169 ( subtract 65 from both sides )
2x² = 104 ( divide both sides by 2 )
x² = 52 ( take the square root of both sides )
x =
=
= ×
= 2
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Given:
The three lengths in the options.
To find:
Which three lengths could be the lengths of the sides of a triangle?
Solution:
If the sum of two smaller sides is greater than the largest side, then the three sides can form a triangle otherwise the triangle is not possible.
In option A, the three sides are 4 cm, 8 cm, 13 cm. Here, the largest side is 13 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option B, the three sides are 13 cm, 11 cm, 23 cm. Here, the largest side is 23 cm.
Sum of two smaller sides is:
So, the triangle is possible.
In option C, the three sides are 5 cm, 18 cm, 12 cm. Here, the largest side is 18 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
In option D, the three sides are 25 cm, 8 cm, 16 cm. Here, the largest side is 25 cm.
Sum of two smaller sides is:
So, the triangle is not possible.
Therefore, the correct option is B. The three lengths 13 cm, 11 cm, 23 cm could be the lengths of the sides of a triangle.