A triangle's perimeter is 81 cm with side lengths in a 4:3:2 ratio. Find the longest side.
Show answer Hide answer
Answer: C. 36 cm
Explanation
Summing the ratio parts four x, three x, and two x yields a total of nine x. Dividing the perimeter of eighty one centimeters by nine gives the scale factor value of nine. Multiplying the largest ratio part four by nine results in the longest side of thirty six centimeters. The perimeter of a triangle is calculated by adding the lengths of all three sides together. Ratio parts share a common multiplier that preserves the relative proportions of the geometric sides. Solving linear equations allows finding unknown side lengths from a total perimeter constraint.
Tailors use proportional ratios to cut fabric panels for triangular garments and decorative banners. Carpenters scale triangular roof trusses while maintaining strict proportional relationships between beams. Map makers apply ratio scaling to represent geographical distances accurately on smaller coordinate grids. Option a corresponds to a different perimeter total or an incorrect ratio multiplier. Option b reflects a calculation error using an incorrect scaling factor for the parts. Option d represents the length of the shortest side rather than the longest side.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Two squares have perimeters of 48 cm and 20 cm. Find the perimeter and diagonal of a square whose area equals their combined sum.
Show answer Hide answer
Answer: B. 13√2 cm
Combining the areas of the two smaller squares yields a total combined area of one hundred sixty-nine. Extracting the square root of one hundred sixty-nine determines the side length of the new square as thirteen. Multip...
Q2. How many rotations will a wheel of diameter 7/11 m make over a distance of 4 km:_________?
Show answer Hide answer
Answer: D. 2000
The circumference of the wheel is calculated by multiplying pi by the given diameter value. Multiplying twenty two over seven by seven over eleventh gives a rolling distance of two meters per rotation. Dividing the total...
Q3. A triangle has a perimeter of 28 cm and an inradius of 2.5 cm. What is its area?
Show answer Hide answer
Answer: D. None of these
The area of a triangle can be found by multiplying the semiperimeter by the inscribed circle radius. Dividing the perimeter of twenty-eight centimeters by two gives a semiperimeter of fourteen centimeters. Multiplying fo...
Q4. A square's perimeter is twice a rectangle's perimeter. The rectangle's area is 480 sq cm. Find the square's area.
Show answer Hide answer
Answer: D. Cannot be determined
Calculating a square's area from a rectangle's perimeter requires knowing specific linear dimensions of both shapes. A constant ratio between perimeters does not provide enough distinct equations to isolate length and br...
Q5. Selling an article for Rs. 1920 yields a percentage profit equal to the percentage loss at Rs. 1280. What selling price yields a 25% profit?
Show answer Hide answer
Answer: A. Rs. 2000
When percentage profit equals percentage loss between two prices the cost price is their exact midpoint average. Averaging nineteen twenty and twelve eighty isolates the original cost price at sixteen hundred rupees. Add...
Q6. An item's price rises by 15%. To keep spending unchanged, by what percentage must a consumer reduce consumption?
Show answer Hide answer
Answer: B. 13 1/23 %
A fifteen percent price increase raises the total cost index of goods from one hundred to one hundred fifteen units. To maintain constant expenditure, the consumer must reduce consumption proportional to the new higher p...