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Question

Let us draw the squares whose areas equal to the areas of the following triangles:
An isosceles triangle whose base is 7 cm. length and the length of each of two equal sides is 5 cm.

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Solution

1) Draw a triangle PQR with sides QR=7 cm cm,PQ=PR=5 cm.
2) Draw a rectangle ARCP with area equal to that of triangle PQR, by choosing length of rectangle as half of base and height same as height of triangle.
[ Here, area of rectangle = length × breadth
=1/2× base × height
= area of triangle]
Now, we can make a square with area equal to that of rectangle and hence equal to area of triangle.
3) Extend CP to CE, such that CE=BC
4) Draw the perpendicular bisector of PE which bisects PE at O.
5) Taking O as center and OD=OE as radius, draw a semicircle.
6) Extend BC which intersects semicircle at F.
7) Draw a square CFGH taking CF as side.
Here, Area of square CFGH= area of rectangle ABCD
= area of PQR

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