F.5 Quadratic equation(2)

2012-09-21 7:45 am

The base and the height of a right-angled triangle are x cm and y cm respectively,where x<y.if the hypotenuse is 29 cm and the perimeter is 70cm,find x and y

回答 (1)

micatkie

2012-09-21 8:23 am

✔ 最佳答案

By Pythagorean theorem :
base² + height² = hypotenuse²
Hence, hypotenuse = √(base² + height²)

√(x² + y²) = 29 ...... [1]
x + y + √(x² + y²) = 70 ...... [2]

[2] - [1] :
x + y = 41
x = 41 - y ...... [3]

Put [3] into [1] :
√[(41 - y)² + y²] = 29
√(1681 - 82y + y² + y²) = 29
[√(1681 - 82y + 2y²)]² = 29²
1681 - 82y + 2y² = 841
2y² - 82y + 840 = 0
y² - 41y + 420 = 0
(y - 20)(y - 21) = 0
y = 20 or y = 21

Put y = 20 into [3] :
y = 41 - (20)
y = 21

Put y = 21 into [3] :
y = 41 - (21)
y = 20 (rejected)

Hence, x = 20and y = 21

參考: micatkie

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