The amount of soil that is needed to cover the garden with a layer of soil is 49 ft². The correct option is C.
What is an isosceles right-angled triangle?
An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally in the triangle.
Therefore, an isosceles right angled triangle will be a right angle triangle with both legs of the triangle measuring exactly the same.
The given triangle is an isosceles right angle triangle. Let the length of the legs of the right-angle triangle be represented by x. Therefore, using the Pythagoras theorem we can write the length as,
x² + x² = 14²
2x² = 14²
√2 · x = 14
x = 14/(√2)
Now, the area of the isosceles right-angle triangle can be written as,
Area of the triangular field
= (1/2) × Height of the triangle × base of the triangle
= (1/2) × 14/(√2) × 14/(√2)
= (14 × 14)/(2 ×√2 × √2)
= 196/4
= 49 ft²
Hence, the amount of soil that is needed to cover the garden with a layer of soil is 49 ft².
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