Question

A rectangle is made up of six squares if the length of the diagonal of onde square is 2 then find the length of diagonal of rectangle

Answer 1

Answer:

✓ 74

Step-by-step explanation:

the length of one square is 2/✓2=✓2

ie the shorter side of the rectangle

the length of the longer side equals 6✓2

let the diagonal length of the rectangle is X

hence X = ✓(✓2)2+(6✓2)2=✓74

Answer 2

Length of diagonal of rectangle=$\sqrt{74} units$

Step-by-step explanation:

Length of diagonal square,=$d=2$units

Let x be the side of square

$x^2+x^2=d^2$

By using Pythagoras theorem

$2x^2=d^2$

$d=x\sqrt 2$

$x=\frac{d}{\sqrt 2}=\frac{2}{\sqrt 2}=\sqrt 2$units

Side of square=Width of rectangle

Width of rectangle=$b=\sqrt 2$units

Rectangle consist of six squares

Therefore, length of rectangle,l=$6\times \sqrt 2=6\sqrt 2$units

Diagonal of rectangle=$\sqrt{l^2+b^2}=\sqrt{(\sqrt 2)^2+(6\sqrt{2})^2}=\sqrt{74} units$

By using Pythagoras theorem

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