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Question

A right angled triangle ABC is constructed with BC = 3 cm and AB + AC = 9 cm. If B is the right angled, then find the length of AC (in cm).
  1. 5

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Solution

The correct option is A 5
The steps to construct the triangle is as follows.

Step 1: The segment BC is drawn.

Step 2: Construct CBX=90.

Step 3: An arc of radius 9 cm (AB+AC) is drawn from B on BX such that BD = 9 cm.

Step 4: The perpendicular bisector (MN) of CD is constructed which intersects BD at point A.

Step 5: A and C are joined.

ABC is the required triangle.

In ABC, let the length of AC be x.
AB+AC=9,AB=9x.

By using Pythogoras' theorem
AB2+BC2=AC2.

(9x)2+32=x29218x+x2+9=x218x+x2x2=98118x=90x=9018x=5.

Thus, the length of AC is 5 cm.

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