Question

A rectangle with diagonals of length 20 com has sides in the ratio 2:1 . Find the area of the triangle.


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Answer 1

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Answer 2

Step-by-step explanation:

Given :-

A rectangle with diagonals of length 20 cm has sides in the ratio 2:1 .

To find :-

Find the area of the triangle ?

Solution :-

Given that

Length of the diagonal of a rectangle = 20 cm

The ratio of the sides of the rectangle = 2:1

Let they be 2X cm and X cm

Let the length of the rectangle (l) = 2X cm

Let the breadth of the rectangle (b) = X cm

We know that

The length of the diagonal of a rectangle is d=√(l²+b²) units

On Substituting these values in the above formula

=> 20 =√[(2X)²+X²]

=> 20 =√(4X²+X²)

=> 20 = √(5X²)

On squaring both sides then

=> (20)² = [√(5X²)]²

=> 400 = 5X²

=> 5X² = 400

=>X² = 400/5

=> X² = 80

=>X =±√80

=> X =±√(16×5)

=> X =±4√5

X can not be negative

=> X = 4√5 cm

Now , 2X = 2×4√5 = 8√5 cm

Length of the rectangle = 8√5 cm

Breadth of the rectangle = 4√5 cm

We know that

Area of a rectangle = lb sq.units

Area of the given rectangle

= (8√5)×(4√5) cm²

=> (8×4)×(√5×√5)

=> 32×5

=> 160 cm²

Area = 169 cm²

Answer:-

Area of the given rectangle for the given problem is 160 cm²

Used formulae:-

• The length of the diagonal of a rectangle is d=√(l²+b²) units

• Area of a rectangle = lb sq.units

• l = length

• b = breadth