Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.

Result

S =  60 cm2

Solution:

a=12 cm u=8+b u2=a2+b2=122+b2  (8+b)2=122+b2 16b=80  b=80/16=5 cm u=a2+b2=122+52=13 cm u=8+b  S=a⋅ b=12⋅ 5=60 cm2a=12 \ \text{cm} \ \\ u=8+b \ \\ u^2=a^2+b^2=12^2 + b^2 \ \\ \ \\ (8+b)^2=12^2 + b^2 \ \\ 16b=80 \ \\ \ \\ b=80/16=5 \ \text{cm} \ \\ u=\sqrt{ a^2+b^2 }=\sqrt{ 12^2+5^2 }=13 \ \text{cm} \ \\ u=8+b \ \\ \ \\ S=a \cdot \ b=12 \cdot \ 5=60 \ \text{cm}^2

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