Question

Гипотенуза прямоугольного треугольника права 10 см. Найдите его катеты , если известно , что один из них на 2 см больше другого. ( это нужно решить с помощью систем уравнений

Answer 1

Пусть 2 катет будет равен - х см, 1 катет - х+2 см.
х+(х+2)=10
х+х+2=10
2х=8
х=4 см ( 2 катет )
4+2=6 см ( 1 катет )

Answer 2

I can help you solve this problem using a system of equations. Here are the steps:

- Let x be the length of the shorter leg and y be the length of the longer leg. Then we have two equations: $$x^2 + y^2 = 10^2$$ and $$y = x + 2$$ - Substitute y with x + 2 in the first equation and simplify: $$x^2 + (x + 2)^2 = 100$$ $$2x^2 + 4x - 96 = 0$$ - Factor the quadratic equation or use the quadratic formula to find x: $$x = -6 \text{ or } x = 8$$ - Reject the negative value of x since it does not make sense for a length. So x = 8 cm. - Substitute x with 8 in the second equation and find y: $$y = 8 + 2$$ $$y = 10 \text{ cm}$$ - The lengths of the legs are 8 cm and 10 cm.

You can also watch some videos on how to solve right triangles using trigonometry , , or . Or you can use some online calculators to check your answers , , or . You can also read some articles on solving right triangles or solving systems of equations by substitution . I hope this helps.how to solve a system of equations for a right triangle