Question

1) The length and breath of a
rectangle are in the ratio 4:3, if
the diagonal measures 25 cm,
then the perimeter of the
rectangle is​

Answer 1

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Perimeter of the rectangle is 50m

Given :-

The ratio of length(l) and breadth(b) of a rectangle = 4:3

The diagonal of the rectangle = 25cm

Formula Applied :-

$( {diagonal})^{2} = ( {length})^{2} + ({breadth})^{2}$

$perimeter = 2(length + breadth)$

To Find :-

Perimeter of the rectangle

Solution :-

There we have ratio of Length and Breadth are in the ration 4:3

hence,

$\frac{l}{b} = \frac{4}{3} \\ 3l = 4b \\ l= \frac{4b}{3}$

We know that

${d}^{2} = {l}^{2} + {b}^{2} \\ ( {25})^{2} = ({ \frac{4b}{3} })^{2} + {b}^{2}</p><p>$

Taking squares on both sides,

$25 = \frac{4b}{3} + b \\ 25 = \frac{4b + 3b}{3} \\ 75 = 7b \\ b = \frac{75}{7}$

Substitute the value of breadth in diagonal formula,

${25}^{2} = {l}^{2} + {b}^{2} \\ 25 = l + ( \frac{75}{7} ) \\ 25 = ( \frac{7l + 75}{7}) \\ 25 \times 7 = 7l + 75 \\ 175 = 7l + 75 \\ 7l = 175 - 75 \\ 7l = 100 \\ l = \frac{100}{7}$

Since ,

$perimeter = 2(l + b) \\ = 2( \frac{100}{7} + \frac{75}{7} ) \\ = 2( \frac{100 + 75}{7}) \\ = 2( \frac{175}{7} ) \\ = \frac{350}{7} \\ = 50m$

Answer 2

Answer:

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