Question

A rectangle has an area of root 80 cm^2 and a breadth of 1 +root 5 cm .Calculate the exact length of the rectangle, leaving your answer as a simplified surd.

Answer 1

Answer:

$length = 5.7 + 0.1cm \\ breadth = 3.4 + 0.2cm \\ A = Lb</p><p>= (5.7×3.4) \\ ∆A= A× (AL/A+ B/B) \\ = 19.38×(0.1/5.7+ 0.2/3.4) \\ = 1.48 {cm}^{2} \\ area \: of \: rectange \\ = (19.38 + 1.48) {cm}^{2}$

Answer 2

Concept Introduction:

Area of rectangle is given by length times its breadth. That is area= length * breadth.

Given: A rectangle has an area of $\sqrt{80} cm^2$ and a breadth of $1 +\sqrt{5}cm$.

To Find:

We have to find the value of, length of rectangle.

Solution:

According to the problem,

Area= length * breadth.

⇒ $\sqrt{80} =(1+\sqrt{5} )*l$

⇒$l=\frac{\sqrt{80} }{1+\sqrt{5} }$

⇒$l=\frac{\sqrt{80}*(\sqrt{5} -1) }{5-1}$$=\frac{4*\sqrt{5}*(\sqrt{5}-1) }{4} =5-\sqrt{5}$ $cm$

Final Answer:

The value of length of rectangle is $\sqrt{5} (\sqrt{5} -1)cm$.

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