Practise the method.
Example 1
In isosceles triangle ABC, AB= AC and DE ∥ BC. AD=34cm and DB=51cm. The lower region DBCE has area 2520cm2. The perpendicular height of triangle ADE is 30cm. Find the perimeter of ABC, in cm.
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Answer: 250
- The linear scale ADE:ABC is 2:5;
- the area scale is 4:25.
- The smaller area is 2520×25−44=480.
- Thus DE=2×30480=32, and BC=32×25=80.
- Each equal side is 34+51=85.
- Perimeter =250cm.
Example 2
Two similar closed rectangular boxes have corresponding lengths in the ratio 2:3. Each box has its three edge lengths in the ratio 1:2:3. Their surface areas differ by 1760cm2. Find the difference in their volumes, in cm3.
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Answer: 7296
- If a box has edges t,2t,3t, its surface area is 22t2 and volume is 6t3.
- The smaller surface area is 1760×9−44=1408
- its shortest edge is √221408=8.
- The larger shortest edge is 12.
- Volume difference =6(123−83)=7296cm3.
Example 3
In isosceles triangle ABC, AB= AC and DE ∥ BC. AD=34cm and DB=51cm. The lower region DBCE has area 2520cm2. The perpendicular height of triangle ADE is 30cm. Find the perimeter of ABC, in cm.
Show worked answer
Answer: 250
- The linear scale ADE:ABC is 2:5;
- the area scale is 4:25.
- The smaller area is 2520×25−44=480.
- Thus DE=2×30480=32, and BC=32×25=80.
- Each equal side is 34+51=85.
- Perimeter =250cm.