the sum of legs for a right triangle be 21 and their product is 40. Find the perimeter of this triangle.

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Mathematics Neala 4 years 2021-07-22T05:20:36+00:00 2021-07-22T05:20:36+00:00 1 Answers 17 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Helga · Answer 1 · 2021-07-22T05:22:23+00:00

Answer:

The perimeter of the triangle is 40.

Step-by-step explanation:

The sum of legs for a right triangle is 12:

$a + b = 21$

$a = 21 - b$ (1)

And their product is:

$a*b = 40$ (2)

By entering eq (1) into (2) we have:

$(21 - b)b = 40$

$21b - b^{2} - 40 = 0$

We can find the value of “b” by solving the above quadratic equation.

$b_{1} = 2.1$

$b_{2} = 18.9$

Since the two values satisfy the equation, we can use either of them to find “a”. We will use b₁.

$a = 21 - 2.1 = 18.9$

Now, the hypotenuse of the right triangle is given by:

$h = \sqrt{a^{2} + b^{2}} = \sqrt{(18.9)^{2} + (2.1)^{2}} = 19$

Hence, the perimeter is:

$P = a + b + h = 18.9 + 2.1 + 19 = 40$

Therefore, the perimeter of the triangle is 40.

I hope it helps you!