Question

Social work aims at fulfilment of human needs. Social workers aim to open the doors of access and opportunity for those who are in greatest need. Free education is a great social work. By doing so, we can remove illiteracy from our society. Raman, being a social worker, wants to donate his land to the Village Panchayat for opening a school. Raman's land is in the form of a rectangle of dimensions 500 m × 400 m. The Village Panchayat decides to leave area on all four sides of the land for grass and flowers. A path of uniform width x m is kept for grass and flowers on all four sides, with an area of 118400 m2.

Based on the given information, answer the following questions.

1. Write a quadratic equation in x to represent the above information. 
2. Find the value of x.
3. Find the perimeter of rectangle PQRS. 
4. For what value of x will the area of the path of uniform width be 93600 m²?

Answer 1

i. \[x^{2}-450x+29600=0\] 

ii. \[x^{2}-450x+29600=0\]

\[\Rightarrow (x-370)(x-80)=0\] so x = 80 m (370 is rejected since 500 – 2x would be negative). 

iii. PQ = \[500-2\times 80=340\ \mathrm{m}\] and QR = \[400-2\times 80=240\ \mathrm{m}\]. 

Perimeter = \[2(340+240)=1160\ \mathrm{m}\] 

iv. \[x^{2}-450x+23400=0\]

\[\Rightarrow (x-390)(x-60)=0\] so x = 60 m (390 is rejected).