Question

the area of a reactangle mirror is 45 in2 and its perimeter is 28 in.what are the dimension of the mirror

Answer 1

Answer:-

Given:

Area of a rectangular mirror = 45 sq. inches

Perimeter of the mirror = 28 inches

Let the length of the mirror be L inches and it's breadth be B inches.

We know that,

• Perimeter of a rectangle = 2(length + breadth)
• Area = length * breadth

So,

★ 2(L + B) = 28

⟹ L + B = 28/2

⟹ L = 14 - B -- equation (1).

Similarly,

★ LB = 45

Substitute L value from equation (1)

⟹ (14 - B)(B) = 45

⟹ 14B - B² = 45

⟹ 0 = B² - 14B + 45

⟹ 0 = B² - 9B - 5B + 45

⟹ 0 = B(B - 9) - 5(B - 9)

⟹ 0 = (B - 5)(B - 9)

★ B - 5 = 0

⟹ B = 5 inches

★ B - 9 = 0

⟹ B = 9 inches

Substitute the values of B in equation (1).

When B = 5,

• L = 14 - 5 = 9 inches

When B = 9,

• L = 14 - 9 = 5 inches.

Length of a rectangle is always greater than the breadth.

So, Length = 9 inches & Breadth = 5 inches

∴ The dimensions of the mirror are 9 inches × 5 inches.

Answer 2

$\huge\bf{\underline{GiVeN;-}}$

• Area of a rectangular mirror is 45 inches² .

• Perimeter of that rectangular mirror is 28 inches .

$\\ \huge\bf{\underline{To\:FiNd;-}}$

• Dimensions of the mirror, i.e.

1. Length of the mirror .
2. Breadth of the mirror .

$\\ \huge\bf{\underline{SoLuTiOn;-}}$

● Let Length & Breadth of the rectangular mirror is l and b respectively .

We know that,

→ Perimeter of the rectangular mirror = 2 (l + b)

→ 28 = 2 (l + b)

→ l + b = 28/2

→ l + b = 14 ------(1)

And

→ Area of the rectangular mirror = l × b

→ l × b = 45

→ l = 45/b

☞ Now putting the value of l in the equation (1), we get

→ 45/b + b = 14

→ (45 + b²) = 14b

→ b² - 14b + 45 = 0

→ b² - 9b - 5b + 45 = 0

→ b (b - 9) - 5 (b - 9) = 0

→ (b - 5) (b - 9) = 0

→ b - 5 = 0 or b - 9 = 0

→ b = 5 or 9

Therefore,

→ l × 5 = 45 or. l × 9 = 45

→ l = 45/5 or l = 45/9

→ l = 9 or 5

◉ But we know that length is always larger than breadth . So,

1. Length is 9 inches .
2. And breadth is 5 inches .