Question

can anyone help me with this and explain me this?​

Answer 1

Answer:

Well, for this you have to do the following:

Let length be 'x' cm, then according to the question, breadth = x-7 cm

It is given that diagonal = 13 cm

We know that corner angles of rectangle are right angle therefore by using Pythagoras Theorem, we can have

13×13 = x² + (x-7)²

169 = x² + x² + 49 - 14x

169 - 49 = 2x² - 14x

120 = 2x² - 14x

Dividing both sides by 2

60 = x² - 7x

x² - 7x - 60 = 0

Now by Middle Term Splitting

x² - 12x + 5x - 60 = 0

x(x-12) + 5(x-12) = 0

(x+5)(x-12) = 0

Hence x = -5 and 12

Since any measurement can't be in negative we will take x = 12

Thus

Length = 12 cm

Breadth = 12-7 = 5 cm

Arigato ^_^

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