# Samtel Papers: Sample Questions 5 - 6 of 6

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## Question number: 5

### Write in Short

Distance between a, b is 60 miles, c is 50 miles from both. Find shortest distance between c and the highway connecting a b. (2004)

### Explanation

• Here, distance between a and b is 60 miles and c is 50 miles from both.
• As c is at the same distance from a and b both, it will be on the line passing through the middle point of a and b. So, we can consider the following figure to know the exact geometry. Design of Isosceles Triangle Based on Given Information Drawing projection (which will be the shortest distance) from point c on line ab we can divide it into two equal parts i. e. 30 miles. The projection is at the right angle on highway ab so it generates two right angle triangles there.
• Considering cda, measure of angle cda is 900.

• Applying Pythagoras theorem,

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• Therefore, shortest distance between c and highway joining a and b will be 40 miles.

## Question number: 6

### Write in Short

Area of 2 squares are in the ratio 2: 1. Find the ratio of their perimeter

### Explanation

• Let the length of both squares be l1 and l2
• Area of square is 4l2 and Perimeter is 4l
• Area of first square = Area of second square =
• Perimeter of first square = Perimeter of second square =
• In the given question,

• To find the ratio of perimeter,

• Thus the ratio of perimeter will be : 1