Question

In isosceles triangle RST shown below, RS = RT,

Mand N are midpoints of RS and RT , respectively,
and MN is drawn. If MN = 3.5 and the perimeter
of RST is 25, determine and state the length of
NT.
​

Answer 1

The length of NT in isosceles triangle RST is 7.

Step-by-step explanation:

In an isosceles triangle, the base angles are congruent, and the sides opposite those angles are also congruent. Let's denote the length of RS (and RT) as r, and the length of MN as m Since M and N are midpoints, MN is parallel to the base, and its length is half the length of the base. Therefore,
`\( m = (r)/(2) \).`

The perimeter of the triangle is the sum of the three sides, so
`\( 2r + r = 25 \) (as RS = RT).` Solving for r, we get
`\( r = (25)/(3) \).`

Now, we know that
`\( m = (r)/(2) \),` so
`\( m = (25)/(6) \)`. Finally, the length of NT is the difference between RT and MN, which is
`\( (25)/(3) - (25)/(6) = 7 \).`Therefore, the length of NT is 7 units.

Answer 2

this is not my account but its rt

Step-by-step explanation: