Two sides of a triangle are 7 cm and 12 cm long…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two sides of a triangle are and long. The third side is a whole number of centimetres. Find the smallest and the largest value it can have.
Need a reminder? The key ideaShow
Angles opposite equal sides are equal, and sides opposite equal angles are equal. The perpendicular from the apex bisects the base and the apex angle. The longer side is opposite the larger angle. Any two sides together are longer than the third, so the third side lies between the difference and the sum of the other two.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The limits. The third side satisfies , that is .
Step 2. Whole numbers. The smallest whole number above is . The largest whole number below is .
Step 3. Check. With : . With : .
Answer: the smallest is and the largest is .
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