Question

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Q. Find the dimensions of the rectangle whose perimeter is 36 m and which is such that the square of the length of diagonal is 170 m^2 .

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Answer 1

Step-by-step explanation:

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Answer 2

Answer

Length = 11m

breadth = 7m

Explanation

Given

Perimeter of the triangle = 36m

Square of the diagonal = 170m²

To Find

Length and breadth of the rectangle

Solution

Let,

length = l

breadth = b

We know that

$\boxed{perimeter = 2(l+b)}$

2(l+b) = 36

l+b = 18

l = 18-b -----(1)

Square of the diagonal = 170m²

Consider the right angle triangle, which is formed by the diagonal with length and breadth of the rectangle

From pythagorus theorem

Diagonal² = length² + breadth²

170 = l²+b²

Put l value

(18-b)² +b² = 170

18² + b² -36b +b² = 170

2b² -36b +324 -170= 0

2b² -36b + 154 = 0

b² -18b + 77 = 0

b² -11b -7b+77 = 0

Factorise it!

b(b-11) -7(b-11) = 0

(b-11)(b-7) = 0

Hence,

b = 11 or b = 7

_________________

If, b = 11

l = 18 - b

l = 18-11

l = 9

If, b = 7

l = 18 - b

l = 18 - 7

l = 11

Since, length > breadth

Length = 11m

breadth = 7m