the area of a reactangle mirror is 45 in2 and its perimeter is 28 in.what are the dimension of the mirror
Answers
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.
- Area of a rectangular mirror is 45 inches² .
- Perimeter of that rectangular mirror is 28 inches .
- Dimensions of the mirror, i.e.
- Length of the mirror .
- Breadth of the mirror .
● 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,
- Length is 9 inches .
- And breadth is 5 inches .