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Question
One side of a rectangle is 12 cm long and its diagonal measure 37 cm. Find the other side and the area of the rectangle.
Solution
One side of the rectangle = 12 cm
Diagonal of the rectangle = 37 cm
The diagonal of a rectangle forms the hypotenuse of a right-angled triangle. The other two sides of the triangle are the length and the breadth of the rectangle.
Now, using Pythagoras’ theorem, we have:
`"(One side)"^2+"(Other side)"^2="(hypotenuse)"^2`
⇒`(12)^2+"(other side)"^2=(37)^2`
⇒`144+(Other side)^2=1369`
⇒`(Other side)^2=1329-144`
⇒`(Other side)^2=1225`
⇒`(Other side)=sqrt1225`
⇒`Other side=35 cm`
Thus, we have:
Length = 35 cm
Breadth = 12 cm
Area of the rectangle=`35xx12=420 cm^2`
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