Question

question no 5 solve it fast

Answer 1

Length = 30 cm.
Breadth = 'b' cm.
Diagonal = 34 cm.

We know that, a diagonal divides a rectangle into 2 congruent right angle triangles.

In a right angle triangle of the rectangle:

We know that,

$diagonal {}^{2} \: = \: length {}^{2} + breadth {}^{2} . \\ on \: substituting \: the \: known \: values \: we \: get \: \\ 34 {}^{2} = 30 {}^{2} + b {}^{2} \\ 1156 = 900 + b {}^{2} \\ 1156 - 900 = b {}^{2} \\ 256 = b {}^{2} \\ \sqrt{} 256 = b \\ 16 = b \\ b = 16 \: cm$
We found that the breadth of the rectangle is 16 cm.

So,

$area \: of \: the \: rectangle = length \times breadth \\ = 30 \times 16 \\ = 480 \: cm {}^{2}$

And,

$perimeter \: of \: the \: rectangle = 2(length + breadth) \\ = 2(30 + 16) \\ = 2(46) \\ = 92.$
Therefore, the area and perimeter are 480
$cm {}^{2}$
and 92 cm respectively.