Question

a pair of adjacent side of a rectangle are in the ratio 3 : 4 if its diagonal is 20 cm find the length of sides and hence the perimeter of the rectangle ​

Answer 1

Answer:

Step-by-step explanation:

Ratio=3:4

so,the pair of adjacent sides are 3x,4x

Pythagorean theorem,

$(3x)^{2}+(4x)^{2}=20^{2}\\9x^{2}+16x^{2}=400\\\\25x^{2}=400\\\\x^{2}=\frac{400}{25}\\\\ x^{2}=16\\\\x=\sqrt{16}\\\\x=4\\\\length=4x=4*4=16cm\\\\breadth=3x=3*4=12cm\\\\Perimeter=2*(l+b)\\\\=2*(16+12)=2*28\\\\=56cm$