A reflecting pool is shaped like a right triangle, with one leg along the wall of a building. The hypotenuse is 9 feet longer than the side along the building. The third side is 7 feet longer than the side along the building. Find the lengths of all three sides of the reflecting pool.
Answers
The lengths of all three sides of the reflecting pool in the shape of a right-angled triangle are 8 ft, 15 ft & 17 ft.
Step-by-step explanation:
It is given that the reflecting pool is in the shape of a right-angled triangle.
Let the leg which is along the wall of the building be “x” ft.
Then, the hypotenuse will be “(x+9)” ft and the third side will be “(x+7)" ft.
By using the formula of Pythagoras theorem for the right-angled triangular reflecting pool, we get
Hypotenuse² = Perpendicular² + Base²
⇒(x+9)² = (x+7)² + x²
⇒ x² + 18x + 81 = x² + 14x + 49 + x²
⇒ x² – 4x – 32 = 0
⇒ x² – 8x + 4x - 32 = 0
⇒ x(x-8) + 4(x-8) = 0
⇒ (x-8)(x+4) = 0
⇒ x = 8 or -4
Neglecting the negative value
⇒ x = 8 ft
∴ Hypotenuse = 8+9 = 17 ft
And,
Third side = 8+7 = 15 ft
Thus, the lengths of all three sides of the reflecting pool are 8 ft, 15 ft and 17 ft.
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