Question

9. If AJKL - ANML, find the values of x and y.

Answer 1

Answer:

x = 35, y = 18

Step-by-step explanation:

Since both triangles are similar, their sides must be proportional with means all of them have a common ratio.

If NM = 16, and KJ = 40. 40/16 is the ratio from ∆NML to ∆JKL. The reciprocal(numerator and denominator flip, the product of a number and it's reciprocal is 1) of this is true from ∆JKL to ∆NML.

Now to find the missing sides you multiply a side by the common ratio to find it's corresponding side length.

Dividing by a number is the same as multiplying by the reciprocal of that number.

40/16 can be reduced to 5/2 or 2 ½ as a mixed fraction.

16/40 can be reduced to 2/5 or 0.4 as a decimal.

Since the scale of ∆JKL is greater than ∆NML, you multiply by 5/2 to get the corresponding side of ∆JKL from ∆NML.

Since the scale of ∆NML is less than ∆JKL, you multiply by 2/5 to get the corresponding side of ∆NNL from ∆JKL.

Therefore x = 14 × 5/2 = 70/2 = 35.

y = 45 × 2/5 = 90/5 = 18.