Question

The difference between the length and breadth of a rectangle is
33 m. If its perimeter is 134 m, then its area is:

Answer 1

Given:

• Difference between the length and breadth of rectangle is 33 m.
• Perimeter of rectangle = 134 m

To find:

• Area of rectangle.

SoluTion:

Let -

• Length of rectangle be L
• Breadth of rectangle be B.

According to the question,

★ Difference between length and breadth of rectangle is 33 m.

$\therefore$ L - B = 33 m...............(1)

★ Perimeter of rectangle is 134 m.

$\therefore$ 2(L + B) = 134

→ L + B = $\dfrac{134}{2}$

→ L + B = 67 m..............(2)

Solving question (1) and (2), we get,

→ 2L = 33 + 67

→ 2L = 100

→ L = $\dfrac{100}{2}$

→ L = 50 m

Now, put the value of L in (1).

→ 50 - B = 33

→ B = 50 - 33

→ B = 17 m

Hence, length and breadth of rectangle are 50 m and 17 m respectively.

$\rule{200}2$

We know that,

Area of rectangle = Length × Breadth

→ Area of rectangle = 50 × 17

→ Area of rectangle = 850 m²

Hence, area of rectangle is 850 m².

Answer 2

$\huge\underline{\mathbb{GIVEN:-}}$

✧ The difference between the length and breadth of a rectangle is  33 m.

✧ Perimeter of the rectangle is 134 m.

$\huge\underline{\mathbb{TO\ FIND:-}}$

✧ The area of the rectangle.

$\huge\underline{\mathbb{SOLUTION:-}}$

✧ Let the length of the rectangle be x m.

✧ Then the breadth of the rectangle is (x - 33) m.

We know,

Perimeter of a rectangle = 2(length + breadth)

A/q,

2[x + (x - 33)] = 134

➝ 2(x + x - 33) = 134

➝ 2(2x - 33) = 134

➝ 2x - 33 = 67

➝ 2x = 100

➝ x = 100/2

➝ x = 50

Now,

➧ The length of the rectangle = x = 50 m.

➧ The breadth of the rectangle = x - 33 = 50 - 33 = 17 m.

We also know,

Area of a rectangle = Length × Breadth

➝ Area =50 × 17

➝ Area = 850 m²

∴ So, the area of the rectangle whose perimeter is 134 m, is 850 m².