Question

HlO MATHS ARYABHATTA,S☺

Q2.The area of a rectangle is equal to 96 square meters. Find the length and width of the rectangle if
its perimeter is equal to 40 meters.


Q3.The height of a triangle is 3 feet longer than its corresponding base. The area of the triangle is

equal to 54 square feet. Find the base and the height of the triangle.


Q4.The product of the first and the third of three consecutive positive numbers is equal to 1

subtracted from the square of the second of these numbers. Find the three numbers.

Answer 1

Hii friends,,,, here is ur answer



2nd. Area = 96cm2.
Perimeter = 40cm.
Let the length be l cm. And breadth be b cm.
ACQ,

2(l+b) = 40
l+b = 80.

lb = 96cm2.

Now,
(l+b)2 = l2+b2+2lb
6400= l2+b2+192.
l2+b2 = 6208.
(l+b) 2 = l2+b2 +2lb
(l+b) 2 = 6208+192.
( l+b) = 80.

Length + breadth = 80 cm.

3rd. Let the base be x cm.
Therefore, height = 3x cm.
ACQ,

1/2 (3x*x)=54
3x2 = 108
X2 = 36
X = 6.

Base = 6cm.
Height = 18cm.


Hope that it will help you

Answer 2

question no. (2):
------------------------

area of the rectangle = 96m^2


l × b = 96 ---(1)


perimeter = 40m

2( l + b ) = 40m

l + b = 20 => l = 20 - b --(2)

put value of l in (1) , we get


( 20 - b) × b = 96


20b - b^2 = 96


b^2 - 20b + 96 = 0


b^2 - 12b - 8b + 96 = 0


b( b - 12) - 8 ( b - 12) = 0

b = 12, 8

since, we the breadth is the shortest side of rectangle , so then b = 8m


from (2) length l = 20 - b = 20 - 8 = 12m


Answer: length = 12m , width = 8m



Question no. (3):
------------------------

let the base of triangle be x feet .


height =( x + 3) feet


area of the triangle = 54 feet^2

base × height/ 2 = 54


x × ( x + 3) / 2 = 54


x^2 + 3x = 108

x^2 + 3x - 108 = 0


x^2 + 12x - 9x - 108 = 0

x( x + 12) - 9 ( x + 12) = 0


x = 9, - 12 , length can't be negative.


so take +ve value of x .

base = x = 9 feet

height = x + 3 = 9 + 3 = 12 feet



Answer: base = 9 feet , height = 12feet

Question no. (4) I think there is mistakes in last question. post correct question then I will answer it .