Question

ii) There is a rectangle whose length is more than its breadth by 7m and the
diagonal is more than the length by 1m. Find the length and its breadth of the
rectangle.
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Answer 1

Step-by-step explanation:

Breadth of Rectangle = x

Length of Rectangle = x + 7

Diagonal = x + 8

By Pythagoras' Theorem =

$(x + 8 ) {}^{2} = (x + 7) {}^{2} + x {}^{2}$

${x}^{2} + 16x + 64 = x {}^{2} + 14x + 49 + {x }^{2}$

${x}^{2} + 16x + 64 = 2x {}^{2} + 14x + 49$

16x - 14x +64-49 = 2x^2-x^2

2x + 15 = x^2

x^2-2x-15 = 0

${x}^{2} - 5x + 3x - 15$

x(x-5) + 3(x-5)

x+3. x - 5

x = -3. x = 5. Answer..