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Answered

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One of the diagonals of a rectangle a 20 cm long. The difference between its length and its width is 4 cm. Find the area of the rectangle?

Sagot :

Answer:

A = 192 cm²

Step-by-step explanation:

Given that,

The length of the diagonal of a rectangle is 20 cm.

The difference between its length and its width is 4 cm.

Let the length is l and width is b.

ATQ,

l-b = 4 ...(1)

Let x is the diagonal of the rectangle such that,

[tex]x^2=l^2+b^2[/tex]

or

[tex]20^2=l^2+b^2\\\\l^2+b^2=400[/tex] ....(2)

Now we need to solve equation (1) and (2).

Squaring equation (1) : [tex]l^2+b^2-2lb=16[/tex]

Put equation (2) in above equation.

[tex]400-2lb=16\\\\400-16=2lb\\\\2lb=384\\\\lb=192[/tex]

Since, the area of the rectangle, A = lb

A = 192 cm²

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