Question

A rectangle has a length of X +5 and a width of X -5 and has an area of 15 square units find the length and width of the rectangle.

Answer 1

Answer:L=11.3

W=1.3

Explanation:

Answer 2

Given :-

• Length of rectangle = x + 5
• width of rectangle = x - 5
• Area of rectangle = 15 unit²

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To find:-

• Actual length and width of rectangle

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Solution:-

So to find actual length and width of rectangle, we need to find value of x.

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we know:-

`\bigstar \boxed{ \rm Area~of \: rectangle = length * width}`

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So:-

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`\hookrightarrow \sf Area~of \: rectangle = length * width \\`

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`\hookrightarrow \sf 15=(x + 5)(x - 5) \\`

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`\hookrightarrow \sf 15=x (x - 5) +5(x - 5)\\`

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`\hookrightarrow \sf 15=x^2 - 5x +5(x - 5)\\`

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`\hookrightarrow \sf 15=x^2 - 5x +5x - 25\\`

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`\hookrightarrow \sf 15=x^2 - \cancel {5x} +\cancel {5x} - 25\\`

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`\hookrightarrow \sf 15=x^2 -0 - 25\\`

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`\hookrightarrow \sf 15=x^2 - 25\\`

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`\hookrightarrow \sf 15 + 25=x^2 \\`

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`\hookrightarrow \sf 15 + 25=x^2 \\`

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`\hookrightarrow \sf 40=x^2 \\`

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`\hookrightarrow \sf x^2 = 40\\`

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`\hookrightarrow \sf x = √(40)\\`

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`\hookrightarrow \sf x = √(2 * 2 * 10)\\`

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`\hookrightarrow \sf x = 2 √(10)\\`

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`\hookrightarrow \sf x = 2 * 3.16\\`

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`\hookrightarrow \sf x = 2 * 3.16\\`

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`\hookrightarrow \bf x = 6.32(approx)\\`

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• Length = x + 5
• Length = 6.32 + 5
• Length = 11.32 (units)

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• Breadth = x - 5
• Breadth = 6.32 - 5
• Breadth = 1.32 (units)