Question

what is the value of a?
diagram of triangle with right angles at q and s, segments 5a and a+64, angle bisector at r
a =
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work it out
not feeling ready yet? these can help:
solve linear equations: mixed review
angle vocabulary
lesson: angle bisectors

Explanation:

Step1: Apply the Angle Bisector Theorem (distance from a point to sides)

Since \(TQ\perp RQ\), \(TS\perp RS\), and \(RT\) is the angle bisector of \(\angle QRS\), then \(TQ = TS\).
So, \(5a=a + 64\).

Step2: Solve the linear equation

Subtract \(a\) from both sides: \(5a-a=a + 64-a\), which gives \(4a=64\).
Divide both sides by \(4\): \(a=\frac{64}{4}\).

Answer:

\(16\)