Question

(c) If the length of a rectangle is reduced by 50% and the breadth is increased by 25%, it takes the shape of a square. Find the ratio of (i) the areas of the rectangle and the square
(ii) the perimeters of the rectangle and the square.



pls no rubbish answer​

Answer 1

Answer:

(i) 1:2.5

(ii) Perimeter of the rectangle = 7B

Perimeter of the square = 10B

Step-by-step explanation:

(i )The percentage the length is reduced = 50%

Percentage the breadth is increased = 25%

Let the length of the square be L and the breadth be B

100% of L - 50% of L

= (100% - 50%) of L = 50% of L = $\frac{L}{2}$

100% of B + 25% of B

= (100% + 25%) of B = 125% of B = $\frac{5B}{4}$

∵ square has both sides equal, then  $\frac{L}{2}$ = $\frac{5B}{4}$

                                                             = 4L = 10B (Cross multiplication!)

                                                            ∴ L = $\frac{5B}{2}$

∵ L =  $\frac{5B}{2}$

LB:$L^{2}$ = B:L (ratio of the areas)

= B:$\frac{5B}{2}$ = 1:2.5

     

(ii) Perimeter of the rectangle = 2(L + B) = 2($\frac{5B}{2}$ +B) = 7B

    Perimeter of the square = 4L = 4 x $\frac{5B}{2}$ = 10B

I KNOW IT WAS TOUGH BUT SOME SIMPLE CALCULATIONS :)