Question

Make an equation for the area of the rectangle. Solve it to find the value of x. Also find the actual length and breadth of rectangle. Also check the answer.​

Answer 1

Step-by-step explanation:

Area of rectangle = l × b

Area = 45

l = 9

b = 3x-4

Area = 9×(3x-4)

45 = 27x-36

45+36 = 27x

81 = 27x

x = 81/27

x = 3

l = 9

b = 3(3)-4 = 5

Area = 9×5 = 45

Answer 2

Step-by-step explanation:

Given:Figure

To find:Make an equation for the area of the rectangle. Solve it to find the value of x. Also find the actual length and breadth of rectangle. Also check the answer.

Solution:

Area of Rectangle= length×breadth

ATQ

length=9 cm [GIVEN]

breadth= (3x-4) cm [GIVEN]

1. Find Equation of area:

As,

Area of Rectangle= length×breadth

Area= 45 cm² [GIVEN]

Put given values

$45 = 9 \times (3x - 4) \\ \\ 3x - 4 = \frac{45}{9} \\ \\ \bold{\green{3x - 4 = 5 }}$

2. Value of x:

$3x - 4 = 5 \\ \\ 3x = 5+ 4 \\ \\ 3x = 9 \\ \\ x = \frac{9}{3} \\ \\ \bold{\blue{x = 3}}$

Thus,

Value of x is 3.

3. Actual length and breadth of rectangle :

Since length of rectangle is independent of x, Thus length is 9 cm

Breadth= 3x-4

put x= 3

Breadth= 3×3-4=9-4=5 cm

4. Verification of answer:

Area of Rectangle by calculated length And breadth

Area= 9×5= 45 cm²...eq1

Given area= 45 cm²...eq2

eq1=eq2

Hence verified.

Hope it helps you.