Jayanti takes the shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges

Solution:

Given, Jayanti takes the shortest route to her home by walking diagonally across a rectangular park.

The measure of the park is 60 metres × 80 metres.

We have to find how much shorter the route across the park is than the route around its edges.

Consider a rectangular park ABCD,

Jayanti travels along the diagonal AC.

The length and breadth of the rectangle is 80 m and 60 m.

Considering right angle triangle ABC,

By Pythagorean theorem,

AC² = AB² + BC²

AC² = 80² + 60²

AC² = 6400 + 3600

AC² = 10000

Taking square root,

AC = 100 m

If Jayanti goes round the edges, the distance covered = 80 + 60 = 140 m

Distance travelled through the diagonal = 100 m

Difference between two paths = 140 - 100

= 40 m

Therefore, the required distance is 40 m.

✦ Try This: Jeni takes the shortest route to her home by walking diagonally across a rectangular park. The park measures 90 metres × 60 metres. How much shorter is the route across the park than the route around its edges?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 114

Jayanti takes the shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges

Summary:

Jayanti takes the shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. The route across the park is shorter than the route around its edges by 40 metres.

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