Final answer:
To solve the proportions k/6 = 8/16 and 5.4/7 = 27/h using the cross products property, we cross multiply and solve for the unknown variables, yielding the solutions k = 3 and h = 35 respectively.
Step-by-step explanation:
To solve the proportions using the cross products property, we need to multiply the numerator of one ratio by the denominator of the other ratio and set that equal to the product of the remaining numerator and denominator. For the first proportion, k/6 = 8/16, we multiply k by 16 and 6 by 8 and set the products equal to each other. The equation is k * 16 = 6 * 8, which simplifies to 16k = 48. To find the value of k, we divide both sides by 16, resulting in k = 3.
For the second proportion, 5.4/7 = 27/h, we cross multiply by multiplying 5.4 by h and 27 by 7. This gives us 5.4 * h = 27 * 7, which simplifies to 5.4h = 189. To find the value of h, we divide both sides by 5.4, resulting in h = 35.