Question

EXERCISE 15 (C) 3 10 12 1. Fill in the blanks for a rectangle: Length (in cm) 5 Breadth (in cm) 5 8 Perimeter (in cm) ? ? ? ? 8 11 15 ? 14 ? ? ? 2 ? ? 42 ? ? Area 96 210 ? 88​

Answer 1

Answer:

Length (in cm): 3, 5, 10, 12, 15, 8, 11

Breadth (in cm): 5, 8, 15, 8, 14, 13, 8

Perimeter (in cm): 16, 26, 50, 40, 58, 42, 38

Area: 15, 40, 150, 96, 210, 104, 88

Step-by-step explanation:

So basically we are provided with the values of length, breadth, area and perimeter of a rectangle. We have to fill in the blanks using the given values.

We know that-

Perimeter of rectangle = 2(length + breadth)

Area of rectangle = length × breadth

The value of length and breadth in the first column is 3 cm (length) and 5 cm (breadth). Similarly, in second and third column the value of length is 5 cm (in second column), 10 cm (in third column) and breadth is 8 cm (in second column), 15 cm (in third column). Simply, substitute these values in the above formulas.

First first column:

→ Perimeter of rectangle = 2(3 + 5) = 2(8) = 16 cm

→ Area of rectangle = 3 × 5 = 15 cm ²

For second column:

→ Perimeter of rectangle = 2(5 + 8) = 2(13) = 26 cm

→ Area of rectangle = 5 × 8 = 40 cm²

For third column:

→ Perimeter of rectangle = 2(10 + 15) = 2(25) = 50 cm

→ Area of rectangle = 10 × 15 = 150 cm²

In the first three columns, we substituted the values of the length and breadth into the formula of area and perimeter of rectangle; to find out their values. But in the rest of the column we can't just substitute; because in rest columns length and breadth values is not given (at some places). So, to find the area and perimeter of a rectangle, we have to assume that the missing value of length or breadth is 'x' cm.

Let's say that the value of breadth in fourth column is x. So,

→ Area of rectangle = 12 × x

→ 96 = 12x

→ 96/12 = x

→ 8 = x

Value of breadth = 8 cm

→ Perimeter of rectangle = 2(12 + 8) = 2(20) = 40 cm

Similarly, for fifth column:

→ Area of rectangle = x × 14

→ 210 = 14x

→ 210/14 = x

→ 15 = x

Value of length = 15 cm

→ Perimeter of rectangle = 2(15 + 14) = 2(29) = 58 cm

For sixth column:

→ Perimeter of rectangle = 2(8 + x)

→ 42 = 2(8 + x)

→ 21 = 8 + x

→ x = 13

Value of breadth = 13 cm

→ Area of rectangle = 8 × 13 = 104 cm²

For seventh column:

→ Area of rectangle = 11 × x

→ 88 = 11x

→ x = 8

Value of breadth = 8 cm

→ Perimeter of rectangle = 2(11 + 8) = 2(19) = 38 cm

Answer 2

Answer:

Step-by-step explanation: