Step-by-step explanation:
the perimeter is easy.
it is an isoceles triangle, that means both sides are equally long (10 units).
the length of the baseline we can read directly off the coordinates of P and Q.
both are on the same horizontal grid line y = 1. so, the difference in x is their distance : 8 - -8 = 8+8 = 16
so, the perimeter is 10 + 10 + 16 = 36 units.
now, for k :
k is the height of the triangle + 1 (as the baseline is at y=1 and not at 0).
we can get the height by using Pythagoras :
c² = a² + b²
c is the Hypotenuse (the baseline) of the dude opposite of the 90° angle.
the triangle we use for this is
PR, half of PQ and the height of the main triangle, with PR being the Hypotenuse.
so,
10² = (16/2)² + height² = 8² + height²
height² = 10² - 8² = 100 - 64 = 36
height = 6
therefore, k = 6 + 1 = 7
