Question(9) If : then (a) (b) (c) (d) (10) If the ratio between areas of two similar triangles equals and the pe the smaller triangle is 60 cm then the perimeter of the greater triangle equals (a) 60 (b) 80 (c) 100 (d) 120
Studdy Solution
STEP 1
1. For problem (9), we assume the trigonometric identity implies .
2. For problem (10), we assume the ratio of areas of similar triangles is the square of the ratio of their corresponding sides, and that the perimeter is proportional to the side lengths.
STEP 2
1. Solve the trigonometric equation for .
2. Determine the perimeter of the greater triangle using the ratio of areas.
STEP 3
For problem (9), use the identity implies .
Given:
Using the identity:
Simplify the equation:
Combine terms:
Multiply both sides by 2:
Subtract from both sides:
Divide by 2:
STEP 4
For problem (10), use the relationship between the areas and perimeters of similar triangles.
Given the ratio of areas is , the ratio of corresponding sides is the square root of the area ratio:
Let be the perimeter of the smaller triangle and be the perimeter of the greater triangle. The ratio of perimeters is the same as the ratio of corresponding sides:
Given cm, solve for :
Cross-multiply to solve for :
Divide by 3:
The solutions are:
For problem (9), .
For problem (10), the perimeter of the greater triangle is cm.
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