can you please help me with this question

Question

ΔABC has side lengths 15 cm, 20 cm, and 25 cm. What could be the side lengths of a triangle similar to ΔABC?

a	7 m, 8 m, and 9 m
b	6 m, 8 m, and 10 m
c	5 cm, 10 cm, and 15 cm
d	30 mm, 40 mm, and 55 mm

Answer 1

Hi Chandreka,

When we say two geometrical shapes are "similar" it means that all their angles are the same. A great visual way to think of this is to take a shape and make it bigger or smaller. If all the angles in two triangles are the same than all their side lengths must have increased/decreased by the same amount.

That is, the ratio between all the sides must remain the same. So algebraically this means a similar triangle to ΔABC will have sides equal to some number x times side A, a side of x times B, and a side of x times C.

The first thing to pay attention to is the fact that not all the side lengths are in the same units. To be able to compare them accurately you must first convert everything into the same unit. So let's convert them all to meters. To do that, you first need to know how many cm and mm are in one meter: 100 cm = 1m = 1,000 mm. So how would you figure out what 15cm is in meters? Well you know that cm are smaller than meters, therefore, when you convert them you will get a smaller number. In fact, conversion is very simple and says that 15cm/100cm = 0.15m. You can do the same with the other two lengths to get 0.2m and 0.25m. When going from millimeters to meters you would divide by 1,000 instead. To go from meters to centimeters, you would multiply by 100.

So now that triangle ABC is in the same units, let's check option A together. Does 0.15 times anything equal 7? Yes, but it's a gross decimal. Can you use that same decimal number multiplied by 0.2 to equal 8? No. Therefore option A cannot be a similar triangle to ΔABC. Do a similar thing with all the other options, making sure they all have the same units.

I hope that helps! Please let me know if you have any other questions.