Answer:
√(17) * s/2 = one of equal sides of triangle
Explanation:
Sorry for my handwriting, but the figure will look somewhat like it.
Given, area of triangle = area of square.
We know ar(tri) = 1/2 * b* h
Also, ar(sq) = side²
It is also given,base of triangle = side of square.
Let us be familiar with the properties:
- All of the sides of square are equal.
- Pythagoras theorem: a² +b² = c²(Only for 90° triangle)
Hence,
- 1/2 * b* h = s²
- [ b = s, given]
- 1/2 * b* h = b²
- 1/2 * h = b
- h = 2b.
- h = 2s.
Draw perpendicular from top vertex to the base (height of triangle)
We get a right angled triangle.
- Property Of Isoceles Triangle: Perpendicular from top vertex to the base divides the triangle into congruent parts.(Well, there's a prove on congruency, do let me know in comments if you need!)
Base of the right angled triangle= side of square / 2 (Reason: c.p.c.t)
By Pythagorean theorem,
(leg1)² +(leg2)² = Hypotenuse ²
Here hyp = one of equal side of triangle = a
leg1 = b1 = b/2 = s/2 (b = s)
leg2 = 2s
On putting values,
- (s/2)² + (2s)² = a²
- s²/4 + 4s² = a²
- (Do LCM and take square root on both sides)
- √(17)* s/2 = a
Abbreviations:
- a =One of Equal side of triangle
- s = Side of Square
- h = height of triangle
- b = base of triangle.