Question

Two perpendiculars of equal lengths are dropped from point R on the lines PQ and PS, if length PQ = 2x - 3 and length PS = x + 4, then what is the value of x?

• A. $\frac{1}{7}$
• B. -3
• C. $-\frac{1}{3}$
• D. 7

Answer 1

The correct option is D 7

Triangles PQR and PSR are congruent by RHS congruency rule

∠Q = ∠S [Right angle]
QR = RS [Given]
PR = PR [common side]

Now, Corresponding parts of congruent triangles are congruent
So, PQ = PS

2x - 3 = x + 4
2x - x = 4 + 3
x = 7