Quiz – 1

Have a look at the diagram below.
Let the side of the square = 2 units.
Now the area of the square = 2*2 = 4 sq.unit
Area of the triangle = (1/2)×2×2=2 sq.unit
Ratio = 4 : 2 = 2 : 1.



Video solution:

let each side of the square be a , then area = a²

As given that The side is increased by 25%, then

New side = 125a/100 = 5a/4

New area = (5a/4)²

Increased area= [(25a^2)/16]−a²

Increase %=[(9a²/16)/a²]*100 % = 56.25%



Video solution:

Let original radius = R, Original area = πR²
New radius = (R/2) and new area = (πR²)/4
Area decrease = πR² - (πR²)/4 = (3/4)πR²

So, Area decreased in percentage = [(3/4)πR²] / [πR²] x 100 = 75%



Video solution:

let length = x and breadth = y then

2(x+y) = 46 => x+y = 23

x²+y² = 17² = 289

now (x+y)² = 23²

=> x²+y²+2xy= 529

=> 289+ 2xy = 529

=> xy = 120

area = xy = 120 sq.cm



Video solution:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

s=(1/2) x (30+14+40) = 42

Area of triangle ABC = √[s(s−a)(s−b)(s−c)]

=√ [42(12)(28)(2)]

= 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m



Video solution:

length of wire = 2πr= 2 x (22/7 ) x 56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88 x 88 = 7744sq cm



Video solution:

The diameter is equal to the shortest side of the rectangle.

So radius= 14/2 = 7cm.

Therefore, area of circle =πr^2=(22/7)×7×7=154cm²



Video solution:

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC = √2x = (1.41x) m.

Saving on 2x metres =(2x-1.41x)= (0.59x) m.

Saving % =(0.59x/2x)*100 = 30% (approx)



Video solution:

Let breadth = x m

Then, length = (x+5)m

x(x+5) = 750

x² + 5x - 750= 0

(x+30)(x-25)= 0

x = 25



Video solution:

Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m



Video solution: