Question

A tree with a height of 4m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 20 m long? Use the words similar, corresponding, or proportion to explain your work.

Answer 1

The height of another tree is 5.33 meter

Solution:

Given that, A tree with a height of 4m casts a shadow 15 m long on the ground

To find: height of another tree that casts a shadow which is 20 m long

Let us assume,

$h_a$ = height of tree = 4 m

$s_a$ = shadow of tree = 15 m

$h_b$ = height of another tree = ?

$s_b$ = shadow of another tree = 20 m

Height of tree divided by shadow of tree is equal to height of another tree divided by shadow of another tree

Then by proportion we get,

$\frac{\text{ height of tree}}{\text{ shadow of tree}} = \frac{\text{ height of another tree}}{\text{ shadow of another tree}}$

$\frac{h_a}{s_a} = \frac{h_b}{s_b}$

Substituting the values we get,

$\frac{4}{15} = \frac{h_b}{20}\\\\h_b = \frac{4 \times 20}{15}\\\\h_b = \frac{80}{15}\\\\h_b=5.33$

Thus height of another tree is 5.33 meter

Answer 2

Using proportional relationship, the height of the second tree that cast a shadow of 20 metre long is approximately 5.3 metres.

What is proportion?

Proportion is an equation that defines that the two given ratios are equivalent to each other.

The situation forms a proportional relationship. Therefore,

height of the first tree = 4m

length of shadow of the first tree = 15 m

length of the shadow of the second tree = 20 m

height of the second tree = x

Hence,

4 / x = 15 / 20

cross multiply

20 × 4 = 15x

80 = 15x

divide both sides by 15

x = 80 / 15

x = 5.33333333333

x = 5.3 m

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