Question

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Answer 1

• The perimeter of the rectangle = 82 m.

Given :

• One side of a rectangle = 20 m.
• The length of the diagonal = 29 m.

To Find :

• The perimeter of the rectangle.

Solution :

According to the question,

Diagonal is given in the question and we know that, rectangle has four right angles that means, a rectangle divided into two right angled triangle.

So,

The length of the rectangle is base.

The given one side of a rectangle is perpendicular.

The given one diagonal is hypotenuse.

By pythogoras theorem,

Let,

The base be x.

Given,

Hypotenuse = 29 m.

Perpendicular = 20 m.

$: \implies \rm {(29 \: m)}^{2} = {(x)}^{2} + {(20 \: m)}^{2} \\ \\ : \implies \rm 841 \: {m}^{2} = {x}^{2} + 400 \: {m}^{2} \\ \\ : \implies \rm {841 \: m}^{2} - {400 \: m}^{2} = {x}^{2} \\ \\ : \implies \rm 441 \: {m}^{2} = {x}^{2} \\ \\ : \implies \rm \sqrt{441 \: {m}^{2} } = x \\ \\ : \implies \rm 21 \: m = x \\ \\ \: \: \therefore \: \: \rm x = 21 \: m$

Hence, the length of the base is 21 m.

Now, we have to find the perimeter of the rectangle.

We know that,

Perimeter of the rectangle = 2(l + b)

Where,

• l = length
• b = breadth

Now we have,

• length = 21 m.

• breadth = 20 m.

$: \implies \rm 2(21 \: m + 20 \: m) \\ \\ : \implies \rm 2(41 \: m) \\ \\ : \implies \rm 2 \times 41 \: m \\ \\ : \implies \rm 82 \: m$

Hence,

The perimeter of the rectangle is 82 m.