Question

EsparThe shorter leg of a right triangle is 7 m shorter than the longer leg. The hypotenuse is 7 m longer than the longer leg. Findthe side lengths of the triangle.entsLength of the shorter leg:Length of the longer leg:ImLength of the hypotenuse:Х$?

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

length of the shorter leg = ?

length of the longer leg = ?

length of the hypotenuse = ?

Step 02:

We must analyze the problem to find the solution.

x = length of the shorter leg

y = length of the longer leg

z = length of the hypotenuse

System of equations:

x = y - 7 (eq.1)

z = y + 7 (eq.2)

z² = x² + y² (eq.3)

eq.2 in eq.3

`\begin{gathered} (y+7)^2=x^2+y^2\text{ } \\ y^2+14y+49=x^2+y^2 \\ 14y+49=x^2 \\ \\ \\ \end{gathered}`

14y + 49 = x²

y - 7 = x * (-14) (eq.1)

14y + 49 = x²

-14y + 98 = -14x (eq.1)

__________________

147 = x² - 14x

x² - 14x - 147 = 0

Step 03:

Quadratic equation:

x² - 14x - 147 = 0

`x=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot1\cdot(-147)}}{2.1}`

`\begin{gathered} x1\text{ = }\frac{-(-14)+28_{}}{2}\text{ = 21} \\ x2=(-(-14)-28)/(2)\text{ }=\text{ -7} \end{gathered}`

x = 21 (positive solution)

x = y - 7

21 + 7 = y

28 = y

z = y + 7 = 28 + 7 = 35

The answer is:

length of the shorter leg = 21

length of the longer leg = 28

length of the hypotenuse = 35