The length of a rectangle is 3 cm more than thrice its breath.Its diagonal is 1 cm more than the length. what are the length and breath of the rectangle?
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Answers
Answer:
Length = 24 cm ✬
✬ Breadth = 7 cm ✬
Step-by-step explanation:
Given:
Length of rectangle is 3 cm more than thrice the breadth.
Diagonal is 1 cm more than length.
To Find:
What are the length & breadth ?
Solution: Let the breadth of rectangle be x cm. Therefore,
➟ Thrice of breadth = 3x cm
Length = 3 more than 3x = 3x + 3
Diagonal = 1 more than length = 3x + 4
We know that the each angle of a rectangle is of 90°. Let's consider in rectangle ABCD
BC = length
AB = breadth
AC = diagonal
∠ABC = 90°
Now consider the right angled ∆ABC , we have
AB {perpendicular}
BC {base}
AC {hypotenuse}
Using Pythagoras theorem
★ H² = Perpendicular² + Base² ★
➮ (3x + 4)² = x² + (3x + 3)²
➮ 3x² + 4² + 2(3x)(4) = x² + 3x² + 3² + 2(3x)(3)
➮ 9x² + 16 + 24x = x² + 9x² + 9 + 18x
➮ 16 – 9 + 24x = x² + 18x
➮ 7 + 24x – 18x = x²
➮ 7 + 6x = x²
➮ 0 = x² – 6x – 7
Using middle term splitting method.
➮ x² + x – 7x – 7
➮ x(x + 1) – 7 (x + 1)
➮ (x + 1) (x – 7)
➮ x = –1 or x = 7
We will take positive because length cannot be negative.
So,
Breadth = x = 7 cm
Length = 3(7) + 3 = 24 cm
Diagonal = 3(7) + 4 = 25
Step-by-step explanation:
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