Question

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Please show your work .

Answer 1

QR=8

Explanation:

When two lines are perpendicular, they form two 90-degree angles. So:

m∠QSR = m∠QSP = 90°

We also know that the line segment PS is congruent to the line segment SR.

Lastly, by the reflexive property, QS is congruent to itself.

Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).

Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).

If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):

`3n-1=5n-7=\\6=2n=\\n=3`

Plug in n to the length of QR:

`5n-7=\\5(3)-7=\\15-7=\\8`

So, QR=8.