Question

Please help me and it's important that the answer is right

Answer 1

AB = 12 cm

Explanation:

We can reduce this problem to the solution of a right angle triangle using the Pythagoras Theorem.

First, draw a line parallel to side AB, and that intersects the radius QB at point "C" (see attached image). Notice that by construction, we have created a right angle triangle PCQ (with right angle at vertex C). This triangle has the legs: PC (which is equal in length to AB), and CQ (of length 7 cm - 2 cm = 5cm). The hypotenuse is PQ which we know by the information they provide is of length 1 cm more than AB: "AB+1".

Now, with this info we write the Pythagorean theorem ( hypotenuse squared = leg1 squared + leg2 squared) and solve for the unknown AB:

`hyp^2=leg_1^2+leg_2^2\\(AB+1)^2=AB^2+5^2\\AB^2+2\,AB+1 =AB^2+25\\AB^2+AB^2+2\,AB=25-1\\2\,AB=24\\AB=(24)/(2) \\AB=12`

Therefore, side AB is 12 cm long