Question

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Answer 1

Question :

The length of a rectangle is twice its breadth. If its length is decrease by 9 cm and breadth is increase by 9 l, the area of the rectangle is increase by 81 sq. cm. Find the length of the rectangle.

To Find :

Find the length of the rectangle.

Solution :

Let Length of rectangle be L.

Breadth of rectangle be B.

And area of rectangle be LB.

$\rule{90}1$

A/Q,

Case 1.

The length of a rectangle is twice its breadth.

• L = 2B. ___( 1 )

$\rule{90}1$

Case 2.

If its length is decrease by 9 cm and breadth is increase by 9 l, the area of the rectangle is increase by 81 sq. cm.

• ( L - 9 )( B + 9 ) = LB + 81.

$\rule{90}1$

Taking Case 2,

$\tt \longmapsto (L- 9)(B + 9) = LB + 81.$

$\tt \longmapsto LB + 9L - 9B - 81= LB + 81.$

$\tt \longmapsto 9(L - B) = 81+ 81.$

$\tt \longmapsto 9(L - B)= 162.$

$\tt\longmapsto L - B= 18. \: \: \: \: \: - (2)$

Putting the value of L in Equation 2, We get.

$\tt\longmapsto L - B= 18.$

$\tt\longmapsto 2B - B = 18.$

$\tt\longmapsto B = 18.$

Now, Putting the value of Breadth ( B ) in Equation ( 1 )

$\tt \longmapsto L= 2B.$

$\tt \longmapsto L = 2 \times 18.$

$\tt \longmapsto L= 36 \: cm.$

Therefore, the Length of rectangle is 36 Cm and breadth is 18 Cm.