Question

Please solve much appreciated

Answer 1

Answer:

• Two equivalent fractions with whole numbers may be 180/150, or 6/5

• The height of the tree is 39.6 feet.

Explanation:

The diagram provides the proportion of the heights to the shadows:

• $\frac{x}{33}=\frac{1.8}{1.5}$

From that you are asked (i) to simplify the fraction of the right side to one with whole numbers.

You can do that in two steps by multiplying both numerator and denominator by 10:

• $\frac{1.8\times 10}{1.5\times 10}=\frac{180}{150}$

You can simplify that fraction if you divide by the greatest common factor of 180 and 150, which is 30:

• $\frac{180/30}{150/30}=\frac{6}{5}$

The second part (ii) asks to find the height of the tree, that is x. To solve for x you can multiply both sides by the denominator of the fraction on the left and then simplify:

$\frac{x}{33}=\frac{6}{5}\\ \\ x=\frac{6\times 33}{5}\\ \\ x=\frac{198}{5}=39.6$

Thus, the height of the three is 39.6 feet.