A rectangular wall 4 meters high and 5 meters wide is to be painted. If the cost of painting the entire wall is $15 per square meter, what will be the total cost?

Mathematics
A rectangular wall 4 meters high and 5 meters wide is to be painted. If the cost of painting the entire wall is $15 per square meter, what will be the total cost?

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Answer

4.5 m

Step 1: Identify the similar triangles.
The large triangle has height hh m (lamp-post) and base 3+2=53 + 2 = 5 m.
The small triangle has height 1.81.8 m (man) and base 22 m.

Step 2: Set up the proportion from similar triangles.

h5=1.82\frac{h}{5} = \frac{1.8}{2}

Step 3: Cross-multiply to solve for hh.

h=1.8×52h = \frac{1.8 \times 5}{2}

Step 4: Calculate the numerator.

1.8×5=91.8 \times 5 = 9

Step 5: Divide by the denominator.

h=92=4.5h = \frac{9}{2} = 4.5

The lamp-post is 4.5\mathbf{4.5} m high.
4.5 m

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Quick Answer

Identify the similar triangles. The large triangle has height h m (lamp-post) and base 3 + 2 = 5 m.

A rectangular wall 4 meters high and 5 meters wide is to be painted. If the cost of painting the entire wall is $15 per square meter, what will be the total cost?
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Identify the similar triangles. The large triangle has height h m (lamp-post) and base 3 + 2 = 5 m. The small triangle has height 1.8 m (man) and base 2 m. Step 2: Set up the proportion from similar triangles. (h)/(5) = (1.8)/(2) Step 3: Cross-multiply to solve for h. h = (1.8 × 5)/(2) Step 4: Calculate the numerator. 1.8 × 5 = 9 Step 5: Divide by the denominator. h = (9)/(2) = 4.5 The lamp-post is 4.5 m high. 4.5 m