Given that these two triangular prisms are similar, find the value of 𝑥.
Since we know these shapes are similar, they have corresponding sides. And we can use those side to set up a proportion and solve. So 29 is corresponding to 14.5. They’re in the same spot. And we can set at equal two the other two corresponding sides.
Now we have to be careful. The numerator, the top number, is from the larger prism. And the denominator, the bottom number, is from the smaller prism. So we need to follow that same pattern. The top should be the side from the larger prism. And the bottom needs to be from the smaller prism. And now we can cross-multiply and solve.
So we take 29 and multiply it by 15.5 and take 14.5 and multiply it by 𝑥. So we have 449.5 is equal to 14.5𝑥. So our last step would be to divide both sides by 14.5. So we get that 31 is equal to 𝑥. Therefore, the value of 𝑥 would be 31 millimeters.
Now there’s actually another way that we could do this. Notice the way we set it up is that we had the numerators be from the larger prism and the dominators were from the smaller prism. We could set it up a little bit differently. Instead of having the larger on the numerator, it could be the left fraction. And then the smallers could be the right fraction. So let’s go through this, because we have to make sure that the corresponding sides go together.
So from the larger prism, we have 29 and 𝑥. It doesn’t matter which we choose. But we just have to follow whatever route that we pick. So let’s say we put 29 on the numerator and 𝑥 on the denominator.
Now we have to decide, okay which number on the smaller prism goes with the 29 that needs to be on the numerator? The 14.5 is corresponding with the 29. So if the 29 is on the numerator, the 14.5 must be on the numerator. And then 𝑥 is on the denominator. So 15.5 must also be on the denominator. And now we cross-multiply. So we have 29 times 15.5 and 14.5 times 𝑥. Multiplying and then dividing still gets us an answer of 31. So once again, the value of 𝑥 is 31 millimeters.