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Answers
Step-by-step explanation:
by pythagorean theorem I got the equations in terms of x and by simplifying I got the value x is 7
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Answer:
Hypotenuse = 10 inches
Perpendicular = 8 inches
Base = 6 inches
Step-by-step explanation:
Since, the triangle given is a right angled triangle. We can apply Pythagoras Theorem here ;
According to this theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
⇒ (2x - 4)² = (x - 1)² + (x + 1)²
[Using Identity : (a ± b)² = a² + b² ± 2ab]
⇒ 4x² + 16 - 16x = x² + 1 - 2x + x² + 1 + 2x
⇒ 4x² - 16x + 16 = 2x² + 2
⇒ 4x² - 2x² - 16x + 16 - 2 = 0
⇒ 2x² - 16x + 14 = 0
⇒ x² - 8x + 7 = 0
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Solving the above equation ;
⇒ x² - 8x + 7 = 0
⇒ x² - x - 7x + 7 = 0
⇒ x ( x - 1 ) - 7 ( x - 1 ) = 0
⇒ ( x - 1 ) ( x - 7 ) = 0
⇒ x = 1 or x = 7
We got two values of x,
Case I : When x = 1,
Length of each side,
⇒ Hypotenuse = 2x - 4
= 2 * 2 - 4
= 4 - 4
= 0
Since, measurement here can't be zero. We will take another value of x.
Case II : When x = 7,
Length of each side,
⇒ Hypotenuse = 2x - 4
= 7 * 2 - 4
= 14 - 4
= 10
⇒ Base = x - 1
= 7 - 1
= 6
⇒ Perpendicular = x + 1
= 7 + 1
= 8
Hence, the length of each side of the triangle are 10 inches, 8 inches and 6 inches respectively.
