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

Answer:

8cm and 15cm

Step-by-step explanation:

Answer 2

Answer:

8 cm and 15 cm.

Step-by-step 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.