Question

Please help. I don’t understand and don’t know what do to.

Answer 1

9514 1404 393

Answer:

  72

Step-by-step explanation:

The triangles are said to be similar. (ΔNPQ ~ ΔRSQ) That means corresponding sides have the same ratio:

  NP/RS = NQ/RQ = PQ/SQ = 24/32 = 21/28 = 3/4

This ratio, or scale factor, also applies to the perimeters of the two triangles.

  perimeter NPQ / perimeter RSQ = 3/4

Using the given expressions for the perimeters, we have ...

  (7x +2)/(10x -4) = 3/4

We can solve this equation in the usual way to find the value of x. Then we can use that value to find the perimeter of ΔNPQ.

  4(7x +2) = 3(10x -4) . . . . . multiply both sides by 4(10x -4)

  28x +8 = 30x -12 . . . . . eliminate parentheses

  20 = 2x . . . . . . . . . . . add 12-28x to both sides

  10 = x . . . . . . . . . . . divide both sides by 10

The perimeter of ΔNPQ is ...

  7x +2 = 7(10) +2 = 72

The perimeter of triangle NPQ is 72 units.