Question

A square and a rectangle have the same perimeter of 120m. Find the side of the square. If the rectangle has breadth 5m less than that of the square, find the length and area of the rectangle.

Answer 1

Answer:

so, length of rectangle= 35 m   and   area of rectangle= 875 m².

Step-by-step explanation:

perimeter of square= 120 m

here, perimeter of square= 4× side

                              120 m= 4× side

                                   side= 120/4 m

                                   side= 30 m

now, breadth of rectangle= 30 m - 5 m

                                           = 25 m

so,perimeter of rectangle= 120 m

here, perimeter of rectangle= 2(l+b)

                                     120 m= 2(l+b)

                                  120/2 m= l+25 m        [∵breadth= 25 m we find it above]

                                 60-25 m= l

therefore, l= 35 m

area of rectangle= length×breadth

                            = 25 m × 35 m

                            = 875 m²

∴ length of rectangle= 35 m   and   area of rectangle= 875 m².

Answer 2

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Question:-

• A square and a rectangle have the same perimeter of 120m.
• Find the side of the square.
• If the rectangle has breadth 5m less than that of the square, find the length and area of the rectangle.

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Solution:

Given:-

• Area of both square and rectangle are same that is 120 m

So ATQ ,

(I) Side of square

$⇢perimeter \: of \: square = 4 \times side \\ \\ ⇢120 = 4 \times side \\ \\ ⇢side = \frac{120}{4} \\ \\ ⇢side = 30m$

So side of square is 30 m

(ii) length and area of rectangle

• Breadth is 30 - 5 = 25

$⇢perimeter \: of \: rectangle = 2 \times (l + b) \\ \\ ⇢120 = 2 \times (l + </strong><strong>2</strong><strong>5</strong><strong>) \\ \\ ⇢120 = </strong><strong>5</strong><strong>0</strong><strong> + 2l \\ \\ ⇢2l = 120 - 10 \\ \\ ⇢2l = </strong><strong>7</strong><strong>0</strong><strong> \\ \\ ⇢l = \frac{</strong><strong>7</strong><strong>0</strong><strong>}{2} \\ \\⇢l =</strong><strong> </strong><strong>3</strong><strong>5</strong><strong>m$

Length is 35 m

$⇢area \: of \: reactangle \: = l \times b \\ \\ ⇢area \: of \: reactangle = </strong><strong>3</strong><strong>5 \times </strong><strong>2</strong><strong>5 \\ \\ ⇢area \: of \: rectangle = </strong><strong>8</strong><strong>7</strong><strong>5</strong><strong> {m}^{2}$

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Answer :-

Side of square is 30 m

Length of rectangle is 35m

Area of rectangle is 875 m^2

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