Question

.20 .Two sisters Sonu and Meenu where having a land, so they decided to donate 5% of their land to an orphanage. The orphanage is planning to build a building in the land which is in a shape of a rectangle whose length is five meters more than its breadth. Both the sisters agreed to give their land whole heartedly. The area of their land is 1000 square meter. Question:(i) the area donated for orphanage is

(a) 55 sq.m

(b)50 sq.m

(c) 51 sq.m

(d) 52 sq.m

Clear selection

Q.20 (ii)the dimensions of the land given to the orphanage is

(a)L= 10m and B=6m

(b) L= 1m and B=5m

(c) L= 10m and B=15m

(d) L= 10m and B=5m

​

Answer 1

Answer:

(I)= 50 square meter

(ii)= L = 10m and B =5m

Answer 2

$\bigstar$ Explanation $\bigstar$

$\leadsto$ Solution:-

Given,

Area of Total land which the sisters had = 1000$\rm m^2$

Percentage of the area given to the orphanage  = 5%

Therefore,

Area of land given to the orphanage = $\rm \frac{5}{100} \times 1000 = 50m^2$

Let the breadth of the rectangular building which is to be built in the land be x meters

Then the length of the building = (x + 5) metres

We know that Area of rectangle = Length $\times$ Breadth

Therefore,

The area of the rectangular building = x(x+5) = $\rm x^2 + 5x$

But the area of land = 50$\rm m^2$

Therefore,

$\rm x^2 + 5x = 50\\x^2 + 5x - 50 = 0\\x^2 + 10x - 5x - 50 = 0\\x(x+10) -5(x+10)=0\\(x+10)(x-5) = 0$

Here either (x+10) can be zero or (x-5) can be zero or both (x+10) and (x-5) are zero

In such cases, you have equate both the terms to zero

Equating (x + 10) to 0

$\rm x + 10 = 0 \implies x = -10$

Here we are getting the breadth in negative terms,

We know that length, breadth, height cannot be in negative terms

Therefore,

x cannot be equal to -10

Equating (x-5) to 0

$\rm x-5 = 0 \implies x =5$

As here we are getting breadth in a positive integer term,

Hence,

Breadth = 5 m

Therefore,

Length = Breadth + 5

Length = 15 m

$\boxed{\rm Length\:of\:the\:land\:is\:15m}$

$\boxed{\rm Breadth\:of\:the\:land\:is\:10m}$