Question

The perimeter of a right triangle is 40 cm, and its hypotenuse measures 17cm. Find the length of each leg.Show the work that leads to your conclusion.

I need this answered quickly so please help me

Answer 1

8cm and 15cm

Explanation:

Answer 2

8 cm and 15 cm.

Explanation:

Let x and y represent length of each leg of right triangle.

We have been given that the perimeter of a right triangle is 40 cm, and its hypotenuse measures 17 cm.

We can represent this information in a system of equations as:

`x+y+17=40...(1)`

`x^2+y^2=17^2...(2)`

From equation (1), we will get:

`x+y+17-17=40-17`

`x+y=23`

`x=23-y`

Substitute this value in equation (2):

`(23-y)^2+y^2=17^2`

`529-46y+2y^2=289`

`2y^2-46y+529=289`

`2y^2-46y+240=0`

`y^2-23y+120=0`

`y^2-15y-8y+120=0`

`y(y-15)-8(y-15)=0`

`(y-15)(y-8)=0`

`y=15\text{ (or) }y=8`

Therefore, the length of the legs of the hypotenuse would be 8 cm and 15 feet.