Question

Directions - For the following problem, write a paragraph proof to justify each step you make. All work must be neat,
easy to read and simple to follow. Number steps if necessary. All work must be in fractional form.
If PT = x, PQ = 3x and SR = x, find PS in terms of x.​

Answer 1

$PS = \frac{4}{3} x$

Solution:

Given PRQ is a triangle.

ST is a line parallel to RQ.

$PT = x, \ PQ = 3x, \ SR=\frac{8}{3}x$

$TQ=PQ-PT$

$TQ=3x -x=2x$

Triangle proportionality theorem,

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

$\frac{PS}{SR} =\frac{PT}{TQ}$

$\frac{PS}{\frac{8}{3} x} =\frac{x}{2x}$

Do cross multiplication, we get

$PS \times 2x=x \times \frac{8}{3} x$

Divide by 2x on both sides, we get

$PS = \frac{4}{3} x$