Question

The adjacent sides of a rectangle are in the ratio 5 ratio 4 find the length and breadth of rectangle if perimeter is 90 cm also.find the length of diagonals.
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❌Kindly Find the length of the Diagonals as rest of the solution is provided to u❌
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Answer 1

Answer:

The adjacent sides of a rectangle are in the ratio 5 ratio 4 find the length and breadth of rectangle if perimeter is 90 cm also.find the length of diagonals

Answer 2

${\bf{Given\::}}$

• The adjacent sides of a rectangle are in the ratio 5 : 4.

• Perimeter of the rectangle is 90 cm.

$\\ {\bf{To\: Find\::}}$

• The length of diagonals.

$\\ {\bf{Solution\::}}$

Let,

• Length of the rectangle is 5x.

• Breadth of the rectangle is 4x.

As we know that,

☛ Perimeter of the rectangle is given as,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Perimeter\:=\:2\:(L\:+\:B)\:}\:{\Large\mid}\:\green\bigstar$

➣ 90 = 2 (5x + 4x)

➣ 90 = 2 × 9x

➣ 90 = 18x

➣ x = $\tt{\dfrac{90}{18}}$

➣ x = $\bf\red{5}$

Hence,

➛ Length of the rectangle = 5x = 5 × 5 = 25 cm

And

➛ Breadth of the rectangle = 4x = 4 × 5 = 20 cm

As we know that,

✯ The length of the both diagonal of a rectangle is same.

So,

☛ Here ABCD is a rectangle and BD is a diagonal, as shown in attachment figure.

Where,

• Length = AB = CD = 25 cm

• Breadth = BC = DA = 20 cm

Now,

☛ Here ∆ ABD is a right angle triangle.

Where,

• DA = Height

• AB = Base

• BD = Hypotenuse

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{(Hypotenuse)^2\:=\:(Height)^2\:+\:(Base)^2\:}\:{\Large\mid}\:\green\bigstar$

➠ (BD)² = (20)² + (25)²

➠ (BD)² = 400 + 625

➠ (BD)² = 1025

➠ BD = $\tt{\sqrt{1025}}$

➠ BD = $\bf\pink{32.01\:cm\:\approx\:32\:cm}$

∴ The length of diagonals of the rectangle is 32 cm.