Answered

Get personalized and accurate responses to your questions with IDNLearn.com. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.

the longer leg of a right triangle is 4 cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. Find the side length of the triangle.length of the shorter leg__cm length of the longer leg__cmlength of the hypotenuse ___cm

Sagot :

Mark, this is the solution:

Let x to represent the length of the shorter leg of the right triangle. Thus,

x + 4 = Longer leg

x + 8 = Hypotenuse

Now, we use the Pythagorean theorem to solve for x, this way:

(x + 8)² = (x + 4)² + x²

x² + 16x + 64 = x² + 8x + 16 + x²

Like terms:

-x² +8x + 48 = 0

Multiplying by -1 at both sides:

x² - 8x - 48 = 0

(x -12) (x + 4) = 0

x1 = 12

x2 = -4

We take x1 because the length of a side can't be a negative value. In consequence, we have:

• Shorter leg = 12 cm

,

• Longer leg = 16 cm

,

• Hypotenuse = 20 cm

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.