Question

The side of a pair of adjacent sides of a rectangle are in ratio 3:4. if its diagonal is 20 cm long then find the length of the sides and hence, the perimetre of the rectangle. ​

Answer 1

${\mathfrak{\large{\pink{hola!}}}}$

Ratio=3:4
Diagonal=20cm
To find:-
•Sides
•Perimeter

1)sides=?

Let's take that diagonal as hypotenuse
of the right angled triangle and let the sides be-
3x and 4x

Now by using the Pythagorean Theorem:-
Hypotenuse ²=Base²+Height ²
20²=(3x)²+(4x)²
400=9x²+16x²
400=25x²
x²=400/25
x=√400/25
x=20/5
x=4cm

Then the sides would be

•3×4
${\blue{Side=12cm}}$

•4×4
$\red{Side=16cm}$

Perimeter=2(l+b)
=2(16+12)
=2(28)
${\green{Perimeter=56cm}}$

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Answer 2

hope it answers your question