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Difficulty: MediumPerimeter and Area of 2D Figures

A rectangular metallic sheet has a length of 2828 inches and a width of 1515 inches. A triangular metallic sheet has the exact same area. If the base of the triangular sheet is 2424 inches, what is its height, in inches?

Answer: 35 inches

Answer

35
The correct height is found by first determining the area of the rectangle (28×15=42028 \times 15 = 420). Since the triangle shares this exact area and has a given base of 2424, solving the triangle area formula 420=12(24)h420 = \frac{1}{2}(24)h yields 12h=42012h = 420, which simplifies to h=35h = 35.

Step-by-Step Solution

1
Calculate the area of the rectangular sheet.
Area = 420 square inches
The area of the rectangle is required to find the area of the triangle, as the problem explicitly states their areas are equal.
2
Set up the area equation for the triangular sheet.
420 = 0.5 * 24 * h
Substituting the known area and base into the triangle area formula allows us to solve for the unknown height.
3
Solve the algebraic equation for the height (h).
h = 35
Simplifying 420 = 12h by dividing both sides by 12 isolates the height variable.

Key Concept

Calculating and equating the area of different 2D figures using standard area formulas.
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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