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A garden is in the shape of a right angled triangle and its area is reduced in a road widening project. A fence is built along a line that is parallel to the hypotenuse to mark the area to be included in the road, leaving a smaller triangle for the garden. There is a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original garden was 35 square metres before the reduction, what is the area (in square metres) of the smaller garden?
  • a)
    16.788
  • b)
    16.567
  • c)
    15.788
  • d)
    14.788
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A garden is in the shape of a right angled triangle and its area is re...
Since DE is parallel to AC, ΔABC is similar to ΔDBE by AAA rule of similarity,
i.e. ΔABC ~ ΔDBE

When two triangles are similar, the ratio of their areas is equal to the ratio of squares of their corresponding sides.


Hence, option 4.
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Most Upvoted Answer
A garden is in the shape of a right angled triangle and its area is re...
Given:
- The garden is in the shape of a right-angled triangle.
- The area of the original garden is 35 square meters.
- A fence is built along a line parallel to the hypotenuse to mark the area included in the road.
- The length of the hypotenuse is reduced by 35%.

To find:
The area of the smaller garden.

Explanation:
Let's assume the original triangle has sides a, b, and c, where c is the hypotenuse. The area of the original triangle (A1) is given as 35 square meters.

Step 1: Finding the length of the hypotenuse (c)
Since the length of the hypotenuse is reduced by 35%, the new length of the hypotenuse (c') is given by:
c' = c - (0.35 * c)

Step 2: Finding the ratio of the lengths of the hypotenuse
The ratio of the lengths of the hypotenuse can be calculated as:
c' / c = (c - (0.35 * c)) / c

Simplifying the above equation,
c' / c = 1 - 0.35 = 0.65

Step 3: Finding the ratio of the areas of the triangles
The ratio of the areas of the triangles can be calculated as the square of the ratio of the lengths of the hypotenuse.
(A1' / A1) = (c' / c)^2 = 0.65^2 = 0.4225

Step 4: Finding the area of the smaller garden (A1')
The area of the smaller garden (A1') can be calculated using the ratio of the areas:
A1' = (A1 * (A1' / A1))
A1' = 35 * 0.4225 = 14.7875 square meters

Therefore, the area of the smaller garden is approximately 14.7875 square meters.

Answer:
The area of the smaller garden is approximately 14.788 square meters.
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A garden is in the shape of a right angled triangle and its area is reduced in a road widening project. A fence is built along a line that is parallel to the hypotenuse to mark the area to be included in the road, leaving a smaller triangle for the garden. There is a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original garden was 35 square metres before the reduction, what is the area (in square metres) of the smaller garden?a)16.788b)16.567c)15.788d)14.788Correct answer is option 'D'. Can you explain this answer?
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